LMFDB - Embedded newform 76.3.g.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(7,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 10x^{2} + 100 $ x^4 - 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.2
Root			$2.73861 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	76.7
Dual form			76.3.g.b.11.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(1.23861 - 0.715113i) q^{3} +4.00000 q^{4} +(-3.73861 - 6.47547i) q^{5} +(2.47723 - 1.43023i) q^{6} +3.76593i q^{7} +8.00000 q^{8} +(-3.47723 + 6.02273i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(1.23861 - 0.715113i) q^{3} +4.00000 q^{4} +(-3.73861 - 6.47547i) q^{5} +(2.47723 - 1.43023i) q^{6} +3.76593i q^{7} +8.00000 q^{8} +(-3.47723 + 6.02273i) q^{9} +(-7.47723 - 12.9509i) q^{10} +14.0793i q^{11} +(4.95445 - 2.86045i) q^{12} +(-3.00000 + 5.19615i) q^{13} +7.53185i q^{14} +(-9.26139 - 5.34706i) q^{15} +16.0000 q^{16} +(-13.4772 - 23.3432i) q^{17} +(-6.95445 + 12.0455i) q^{18} +(18.7158 + 3.27374i) q^{19} +(-14.9545 - 25.9019i) q^{20} +(2.69306 + 4.66452i) q^{21} +28.1587i q^{22} +(-21.6475 - 12.4982i) q^{23} +(9.90890 - 5.72091i) q^{24} +(-15.4545 + 26.7679i) q^{25} +(-6.00000 + 10.3923i) q^{26} +22.8185i q^{27} +15.0637i q^{28} +(1.73861 - 3.01137i) q^{29} +(-18.5228 - 10.6941i) q^{30} -39.4565i q^{31} +32.0000 q^{32} +(10.0683 + 17.4388i) q^{33} +(-26.9545 - 46.6865i) q^{34} +(24.3861 - 14.0793i) q^{35} +(-13.9089 + 24.0909i) q^{36} +3.38613 q^{37} +(37.4317 + 6.54749i) q^{38} +8.58136i q^{39} +(-29.9089 - 51.8037i) q^{40} +(-4.45445 - 7.71534i) q^{41} +(5.38613 + 9.32905i) q^{42} +(-45.3861 + 26.2037i) q^{43} +56.3173i q^{44} +52.0000 q^{45} +(-43.2950 - 24.9964i) q^{46} +(19.1703 + 11.0680i) q^{47} +(19.8178 - 11.4418i) q^{48} +34.8178 q^{49} +(-30.9089 + 53.5358i) q^{50} +(-33.3861 - 19.2755i) q^{51} +(-12.0000 + 20.7846i) q^{52} +(41.9545 - 72.6672i) q^{53} +45.6370i q^{54} +(91.1703 - 52.6372i) q^{55} +30.1274i q^{56} +(25.5228 - 9.32905i) q^{57} +(3.47723 - 6.02273i) q^{58} +(-22.2386 + 12.8395i) q^{59} +(-37.0455 - 21.3883i) q^{60} +(-13.7386 + 23.7960i) q^{61} -78.9129i q^{62} +(-22.6812 - 13.0950i) q^{63} +64.0000 q^{64} +44.8634 q^{65} +(20.1366 + 34.8777i) q^{66} +(32.0109 + 18.4815i) q^{67} +(-53.9089 - 93.3730i) q^{68} -35.7505 q^{69} +(48.7723 - 28.1587i) q^{70} +(89.3406 - 51.5808i) q^{71} +(-27.8178 + 48.1819i) q^{72} +(4.45445 + 7.71534i) q^{73} +6.77226 q^{74} +44.2067i q^{75} +(74.8634 + 13.0950i) q^{76} -53.0217 q^{77} +17.1627i q^{78} +(-111.909 + 64.6106i) q^{79} +(-59.8178 - 103.607i) q^{80} +(-14.9772 - 25.9413i) q^{81} +(-8.90890 - 15.4307i) q^{82} +27.1743i q^{83} +(10.7723 + 18.6581i) q^{84} +(-100.772 + 174.543i) q^{85} +(-90.7723 + 52.4074i) q^{86} -4.97322i q^{87} +112.635i q^{88} +(-64.2495 + 111.283i) q^{89} +104.000 q^{90} +(-19.5683 - 11.2978i) q^{91} +(-86.5901 - 49.9928i) q^{92} +(-28.2158 - 48.8713i) q^{93} +(38.3406 + 22.1359i) q^{94} +(-48.7723 - 133.433i) q^{95} +(39.6356 - 22.8836i) q^{96} +(-53.0228 - 91.8381i) q^{97} +69.6356 q^{98} +(-84.7961 - 48.9570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 - 6 * q^3 + 16 * q^4 - 4 * q^5 - 12 * q^6 + 32 * q^8 + 8 * q^9	$ 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9} - 8 q^{10} - 24 q^{12} - 12 q^{13} - 48 q^{15} + 64 q^{16} - 32 q^{17} + 16 q^{18} + 42 q^{19} - 16 q^{20} - 44 q^{21} + 12 q^{23} - 48 q^{24} - 18 q^{25} - 24 q^{26} - 4 q^{29} - 96 q^{30} + 128 q^{32} + 106 q^{33} - 64 q^{34} - 12 q^{35} + 32 q^{36} - 96 q^{37} + 84 q^{38} - 32 q^{40} + 26 q^{41} - 88 q^{42} - 72 q^{43} + 208 q^{45} + 24 q^{46} - 96 q^{48} - 36 q^{49} - 36 q^{50} - 24 q^{51} - 48 q^{52} + 124 q^{53} + 288 q^{55} + 124 q^{57} - 8 q^{58} - 78 q^{59} - 192 q^{60} - 44 q^{61} + 216 q^{63} + 256 q^{64} + 48 q^{65} + 212 q^{66} - 102 q^{67} - 128 q^{68} - 384 q^{69} - 24 q^{70} + 204 q^{71} + 64 q^{72} - 26 q^{73} - 192 q^{74} + 168 q^{76} + 248 q^{77} - 360 q^{79} - 64 q^{80} - 38 q^{81} + 52 q^{82} - 176 q^{84} - 184 q^{85} - 144 q^{86} - 16 q^{89} + 416 q^{90} - 144 q^{91} + 48 q^{92} - 80 q^{93} + 24 q^{95} - 192 q^{96} - 234 q^{97} - 72 q^{98} - 624 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 - 6 * q^3 + 16 * q^4 - 4 * q^5 - 12 * q^6 + 32 * q^8 + 8 * q^9 - 8 * q^10 - 24 * q^12 - 12 * q^13 - 48 * q^15 + 64 * q^16 - 32 * q^17 + 16 * q^18 + 42 * q^19 - 16 * q^20 - 44 * q^21 + 12 * q^23 - 48 * q^24 - 18 * q^25 - 24 * q^26 - 4 * q^29 - 96 * q^30 + 128 * q^32 + 106 * q^33 - 64 * q^34 - 12 * q^35 + 32 * q^36 - 96 * q^37 + 84 * q^38 - 32 * q^40 + 26 * q^41 - 88 * q^42 - 72 * q^43 + 208 * q^45 + 24 * q^46 - 96 * q^48 - 36 * q^49 - 36 * q^50 - 24 * q^51 - 48 * q^52 + 124 * q^53 + 288 * q^55 + 124 * q^57 - 8 * q^58 - 78 * q^59 - 192 * q^60 - 44 * q^61 + 216 * q^63 + 256 * q^64 + 48 * q^65 + 212 * q^66 - 102 * q^67 - 128 * q^68 - 384 * q^69 - 24 * q^70 + 204 * q^71 + 64 * q^72 - 26 * q^73 - 192 * q^74 + 168 * q^76 + 248 * q^77 - 360 * q^79 - 64 * q^80 - 38 * q^81 + 52 * q^82 - 176 * q^84 - 184 * q^85 - 144 * q^86 - 16 * q^89 + 416 * q^90 - 144 * q^91 + 48 * q^92 - 80 * q^93 + 24 * q^95 - 192 * q^96 - 234 * q^97 - 72 * q^98 - 624 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000			1.00000
$2$	2.00000			1.00000
$3$	1.23861	−	0.715113i	0.412871	−	0.238371i	−0.279152	−	0.960247i	$-0.590053\pi$
$3$	1.23861	−	0.715113i	0.412871	−	0.238371i	0.692023	+	0.721876i	$0.256720\pi$
$4$	4.00000			1.00000
$5$	−3.73861	−	6.47547i	−0.747723	−	1.29509i	−0.948912	−	0.315541i	$-0.897814\pi$
$5$	−3.73861	−	6.47547i	−0.747723	−	1.29509i	0.201189	−	0.979552i	$-0.435519\pi$
$6$	2.47723	−	1.43023i	0.412871	−	0.238371i
$7$			3.76593i			0.537989i	0.963142	+	0.268995i	$0.0866914\pi$
$7$			3.76593i			0.537989i	−0.963142	+	0.268995i	$0.913309\pi$
$8$	8.00000			1.00000
$9$	−3.47723	+	6.02273i	−0.386358	+	0.669192i
$10$	−7.47723	−	12.9509i	−0.747723	−	1.29509i
$11$			14.0793i			1.27994i	0.768400	+	0.639970i	$0.221053\pi$
$11$			14.0793i			1.27994i	−0.768400	+	0.639970i	$0.778947\pi$
$12$	4.95445	−	2.86045i	0.412871	−	0.238371i
$13$	−3.00000	+	5.19615i	−0.230769	+	0.399704i	−0.958035	−	0.286652i	$-0.907458\pi$
$13$	−3.00000	+	5.19615i	−0.230769	+	0.399704i	0.727265	+	0.686356i	$0.240791\pi$
$14$			7.53185i			0.537989i
$15$	−9.26139	−	5.34706i	−0.617426	−	0.356471i
$16$	16.0000			1.00000
$17$	−13.4772	−	23.3432i	−0.792778	−	1.37313i	−0.924241	−	0.381811i	$-0.875301\pi$
$17$	−13.4772	−	23.3432i	−0.792778	−	1.37313i	0.131463	−	0.991321i	$-0.458033\pi$
$18$	−6.95445	+	12.0455i	−0.386358	+	0.669192i
$19$	18.7158	+	3.27374i	0.985044	+	0.172302i
$19$	18.7158	+	3.27374i	0.985044	+	0.172302i
$20$	−14.9545	−	25.9019i	−0.747723	−	1.29509i
$21$	2.69306	+	4.66452i	0.128241	+	0.222120i
$22$			28.1587i			1.27994i
$23$	−21.6475	−	12.4982i	−0.941196	−	0.543400i	−0.0508612	−	0.998706i	$-0.516197\pi$
$23$	−21.6475	−	12.4982i	−0.941196	−	0.543400i	−0.890335	+	0.455306i	$0.849530\pi$
$24$	9.90890	−	5.72091i	0.412871	−	0.238371i
$25$	−15.4545	+	26.7679i	−0.618178	+	1.07072i
$26$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$27$			22.8185i			0.845129i
$28$			15.0637i			0.537989i
$29$	1.73861	−	3.01137i	0.0599522	−	0.103840i	−0.834492	−	0.551021i	$-0.814239\pi$
$29$	1.73861	−	3.01137i	0.0599522	−	0.103840i	0.894444	+	0.447181i	$0.147572\pi$
$30$	−18.5228	−	10.6941i	−0.617426	−	0.356471i
$31$		−	39.4565i		−	1.27279i	−0.771364	−	0.636394i	$-0.780425\pi$
$31$		−	39.4565i		−	1.27279i	0.771364	−	0.636394i	$-0.219575\pi$
$32$	32.0000			1.00000
$33$	10.0683	+	17.4388i	0.305101	+	0.528450i
$34$	−26.9545	−	46.6865i	−0.792778	−	1.37313i
$35$	24.3861	−	14.0793i	0.696747	−	0.402267i
$36$	−13.9089	+	24.0909i	−0.386358	+	0.669192i
$37$	3.38613			0.0915170			0.0457585	−	0.998953i	$-0.485430\pi$
$37$	3.38613			0.0915170			0.0457585	+	0.998953i	$0.485430\pi$
$38$	37.4317	+	6.54749i	0.985044	+	0.172302i
$39$			8.58136i			0.220035i
$40$	−29.9089	−	51.8037i	−0.747723	−	1.29509i
$41$	−4.45445	−	7.71534i	−0.108645	−	0.188179i	0.806576	−	0.591130i	$-0.201318\pi$
$41$	−4.45445	−	7.71534i	−0.108645	−	0.188179i	−0.915222	+	0.402951i	$0.867985\pi$
$42$	5.38613	+	9.32905i	0.128241	+	0.222120i
$43$	−45.3861	+	26.2037i	−1.05549	+	0.609388i	−0.924182	−	0.381953i	$-0.875252\pi$
$43$	−45.3861	+	26.2037i	−1.05549	+	0.609388i	−0.131310	+	0.991341i	$0.541918\pi$
$44$			56.3173i			1.27994i
$45$	52.0000			1.15556
$46$	−43.2950	−	24.9964i	−0.941196	−	0.543400i
$47$	19.1703	+	11.0680i	0.407879	+	0.235489i	0.689878	−	0.723926i	$-0.257664\pi$
$47$	19.1703	+	11.0680i	0.407879	+	0.235489i	−0.281999	+	0.959415i	$0.590998\pi$
$48$	19.8178	−	11.4418i	0.412871	−	0.238371i
$49$	34.8178			0.710567
$50$	−30.9089	+	53.5358i	−0.618178	+	1.07072i
$51$	−33.3861	−	19.2755i	−0.654630	−	0.377951i
$52$	−12.0000	+	20.7846i	−0.230769	+	0.399704i
$53$	41.9545	−	72.6672i	0.791593	−	1.37108i	−0.133387	−	0.991064i	$-0.542585\pi$
$53$	41.9545	−	72.6672i	0.791593	−	1.37108i	0.924980	−	0.380016i	$-0.124081\pi$
$54$			45.6370i			0.845129i
$55$	91.1703	−	52.6372i	1.65764	−	0.957040i
$56$			30.1274i			0.537989i
$57$	25.5228	−	9.32905i	0.447768	−	0.163667i
$58$	3.47723	−	6.02273i	0.0599522	−	0.103840i
$59$	−22.2386	+	12.8395i	−0.376926	+	0.217618i	−0.676480	−	0.736461i	$-0.736495\pi$
$59$	−22.2386	+	12.8395i	−0.376926	+	0.217618i	0.299554	+	0.954079i	$0.403162\pi$
$60$	−37.0455	−	21.3883i	−0.617426	−	0.356471i
$61$	−13.7386	+	23.7960i	−0.225223	+	0.390098i	−0.956386	−	0.292105i	$-0.905644\pi$
$61$	−13.7386	+	23.7960i	−0.225223	+	0.390098i	0.731163	+	0.682203i	$0.238978\pi$
$62$		−	78.9129i		−	1.27279i
$63$	−22.6812	−	13.0950i	−0.360018	−	0.207857i
$64$	64.0000			1.00000
$65$	44.8634			0.690205
$66$	20.1366	+	34.8777i	0.305101	+	0.528450i
$67$	32.0109	+	18.4815i	0.477774	+	0.275843i	0.719488	−	0.694504i	$-0.244376\pi$
$67$	32.0109	+	18.4815i	0.477774	+	0.275843i	−0.241714	+	0.970347i	$0.577710\pi$
$68$	−53.9089	−	93.3730i	−0.792778	−	1.37313i
$69$	−35.7505			−0.518123
$70$	48.7723	−	28.1587i	0.696747	−	0.402267i
$71$	89.3406	−	51.5808i	1.25832	−	0.726490i	0.285571	−	0.958358i	$-0.407817\pi$
$71$	89.3406	−	51.5808i	1.25832	−	0.726490i	0.972747	+	0.231867i	$0.0744836\pi$
$72$	−27.8178	+	48.1819i	−0.386358	+	0.669192i
$73$	4.45445	+	7.71534i	0.0610199	+	0.105690i	0.894922	−	0.446224i	$-0.147231\pi$
$73$	4.45445	+	7.71534i	0.0610199	+	0.105690i	−0.833902	+	0.551913i	$0.813898\pi$
$74$	6.77226			0.0915170
$75$			44.2067i			0.589423i
$76$	74.8634	+	13.0950i	0.985044	+	0.172302i
$77$	−53.0217			−0.688594
$78$			17.1627i			0.220035i
$79$	−111.909	+	64.6106i	−1.41657	+	0.817856i	−0.995996	−	0.0894026i	$-0.971504\pi$
$79$	−111.909	+	64.6106i	−1.41657	+	0.817856i	−0.420573	+	0.907259i	$0.638171\pi$
$80$	−59.8178	−	103.607i	−0.747723	−	1.29509i
$81$	−14.9772	−	25.9413i	−0.184904	−	0.320263i
$82$	−8.90890	−	15.4307i	−0.108645	−	0.188179i
$83$			27.1743i			0.327401i	0.986510	+	0.163701i	$0.0523431\pi$
$83$			27.1743i			0.327401i	−0.986510	+	0.163701i	$0.947657\pi$
$84$	10.7723	+	18.6581i	0.128241	+	0.222120i
$85$	−100.772	+	174.543i	−1.18556	+	2.05344i
$86$	−90.7723	+	52.4074i	−1.05549	+	0.609388i
$87$		−	4.97322i		−	0.0571635i
$88$			112.635i			1.27994i
$89$	−64.2495	+	111.283i	−0.721904	+	1.25037i	0.238331	+	0.971184i	$0.423400\pi$
$89$	−64.2495	+	111.283i	−0.721904	+	1.25037i	−0.960236	+	0.279191i	$0.909934\pi$
$90$	104.000			1.15556
$91$	−19.5683	−	11.2978i	−0.215037	−	0.124151i
$92$	−86.5901	−	49.9928i	−0.941196	−	0.543400i
$93$	−28.2158	−	48.8713i	−0.303396	−	0.525497i
$94$	38.3406	+	22.1359i	0.407879	+	0.235489i
$95$	−48.7723	−	133.433i	−0.513392	−	1.40456i
$96$	39.6356	−	22.8836i	0.412871	−	0.238371i
$97$	−53.0228	−	91.8381i	−0.546627	−	0.946785i	−0.998503	−	0.0547042i	$-0.982578\pi$
$97$	−53.0228	−	91.8381i	−0.546627	−	0.946785i	0.451876	−	0.892081i	$-0.350755\pi$
$98$	69.6356			0.710567
$99$	−84.7961	−	48.9570i	−0.856526	−	0.494515i
$100$	−61.8178	+	107.072i	−0.618178	+	1.07072i
$101$	66.9425	−	115.948i	0.662797	−	1.14800i	−0.317080	−	0.948399i	$-0.602702\pi$
$101$	66.9425	−	115.948i	0.662797	−	1.14800i	0.979877	−	0.199600i	$-0.0639643\pi$
$102$	−66.7723	−	38.5510i	−0.654630	−	0.377951i
$103$			103.477i			1.00463i	0.864684	+	0.502316i	$0.167519\pi$
$103$			103.477i			1.00463i	−0.864684	+	0.502316i	$0.832481\pi$
$104$	−24.0000	+	41.5692i	−0.230769	+	0.399704i
$105$	20.1366	−	34.8777i	0.191778	−	0.332169i
$106$	83.9089	−	145.334i	0.791593	−	1.37108i
$107$			67.7867i			0.633520i	0.948506	+	0.316760i	$0.102595\pi$
$107$			67.7867i			0.633520i	−0.948506	+	0.316760i	$0.897405\pi$
$108$			91.2739i			0.845129i
$109$	24.8634	+	43.0646i	0.228104	+	0.395088i	0.957246	−	0.289274i	$-0.0934140\pi$
$109$	24.8634	+	43.0646i	0.228104	+	0.395088i	−0.729142	+	0.684362i	$0.760081\pi$
$110$	182.341	−	105.274i	1.65764	−	0.957040i
$111$	4.19410	−	2.42147i	0.0377847	−	0.0218150i
$112$			60.2548i			0.537989i
$113$	−70.9089			−0.627512			−0.313756	−	0.949504i	$-0.601587\pi$
$113$	−70.9089			−0.627512			−0.313756	+	0.949504i	$0.601587\pi$
$114$	51.0455	−	18.6581i	0.447768	−	0.163667i
$115$			186.904i			1.62525i
$116$	6.95445	−	12.0455i	0.0599522	−	0.103840i
$117$	−20.8634	−	36.1364i	−0.178319	−	0.308858i
$118$	−44.4772	+	25.6789i	−0.376926	+	0.217618i
$119$	87.9089	−	50.7542i	0.738730	−	0.426506i
$120$	−74.0911	−	42.7765i	−0.617426	−	0.356471i
$121$	−77.2277			−0.638246
$122$	−27.4772	+	47.5920i	−0.225223	+	0.390098i
$123$	−11.0347	−	6.37088i	−0.0897128	−	0.0517957i
$124$		−	157.826i		−	1.27279i
$125$	44.1822			0.353458
$126$	−45.3623	−	26.1899i	−0.360018	−	0.207857i
$127$	20.2039	+	11.6647i	0.159086	+	0.0918484i	0.577430	−	0.816441i	$-0.304056\pi$
$127$	20.2039	+	11.6647i	0.159086	+	0.0918484i	−0.418343	+	0.908289i	$0.637389\pi$
$128$	128.000			1.00000
$129$	−37.4772	+	64.9125i	−0.290521	+	0.503197i
$130$	89.7267			0.690205
$131$	23.9436	−	13.8238i	0.182775	−	0.105525i	−0.405821	−	0.913953i	$-0.633014\pi$
$131$	23.9436	−	13.8238i	0.182775	−	0.105525i	0.588596	+	0.808427i	$0.299681\pi$
$132$	40.2733	+	69.7554i	0.305101	+	0.528450i
$133$	−12.3287	+	70.4825i	−0.0926968	+	0.529943i
$134$	64.0217	+	36.9630i	0.477774	+	0.275843i
$135$	147.760	−	85.3095i	1.09452	−	0.631922i
$136$	−107.818	−	186.746i	−0.792778	−	1.37313i
$137$	99.4089	−	172.181i	0.725612	−	1.25680i	−0.233109	−	0.972451i	$-0.574890\pi$
$137$	99.4089	−	172.181i	0.725612	−	1.25680i	0.958721	−	0.284347i	$-0.0917768\pi$
$138$	−71.5010			−0.518123
$139$	232.738	+	134.371i	1.67437	+	0.966699i	0.965144	+	0.261718i	$0.0842891\pi$
$139$	232.738	+	134.371i	1.67437	+	0.966699i	0.709227	+	0.704981i	$0.249044\pi$
$140$	97.5445	−	56.3173i	0.696747	−	0.402267i
$141$	31.6594			0.224535
$142$	178.681	−	103.162i	1.25832	−	0.726490i
$143$	−73.1584	−	42.2380i	−0.511597	−	0.295371i
$144$	−55.6356	+	96.3637i	−0.386358	+	0.669192i
$145$	−26.0000			−0.179310
$146$	8.90890	+	15.4307i	0.0610199	+	0.105690i
$147$	43.1258	−	24.8987i	0.293373	−	0.169379i
$148$	13.5445			0.0915170
$149$	36.2158	+	62.7277i	0.243059	+	0.420991i	0.961584	−	0.274510i	$-0.0885157\pi$
$149$	36.2158	+	62.7277i	0.243059	+	0.420991i	−0.718525	+	0.695501i	$0.755182\pi$
$150$			88.4135i			0.589423i
$151$		−	39.4565i		−	0.261301i	−0.991428	−	0.130651i	$-0.958293\pi$
$151$		−	39.4565i		−	0.261301i	0.991428	−	0.130651i	$-0.0417066\pi$
$152$	149.727	+	26.1899i	0.985044	+	0.172302i
$153$	187.453			1.22519
$154$	−106.043			−0.688594
$155$	−255.499	+	147.512i	−1.64838	+	0.951693i
$156$			34.3254i			0.220035i
$157$	−50.9545	−	88.2557i	−0.324551	−	0.562138i	0.656871	−	0.754003i	$-0.271880\pi$
$157$	−50.9545	−	88.2557i	−0.324551	−	0.562138i	−0.981421	+	0.191865i	$0.938546\pi$
$158$	−223.818	+	129.221i	−1.41657	+	0.817856i
$159$		−	120.009i		−	0.754772i
$160$	−119.636	−	207.215i	−0.747723	−	1.29509i
$161$	47.0673	−	81.5229i	0.292343	−	0.506354i
$162$	−29.9545	−	51.8826i	−0.184904	−	0.320263i
$163$		−	190.563i		−	1.16910i	−0.811358	−	0.584550i	$-0.801271\pi$
$163$		−	190.563i		−	1.16910i	0.811358	−	0.584550i	$-0.198729\pi$
$164$	−17.8178	−	30.8613i	−0.108645	−	0.188179i
$165$	75.2831	−	130.394i	0.456261	−	0.790268i
$166$			54.3486i			0.327401i
$167$	−256.681	−	148.195i	−1.53701	−	0.887395i	−0.999012	−	0.0444508i	$-0.985846\pi$
$167$	−256.681	−	148.195i	−1.53701	−	0.887395i	−0.538001	−	0.842944i	$-0.680820\pi$
$168$	21.5445	+	37.3162i	0.128241	+	0.222120i
$169$	66.5000	+	115.181i	0.393491	+	0.681547i
$170$	−201.545	+	349.085i	−1.18556	+	2.05344i
$171$	−84.7961	+	101.337i	−0.495883	+	0.592614i
$172$	−181.545	+	104.815i	−1.05549	+	0.609388i
$173$	113.863	+	197.217i	0.658170	+	1.13998i	0.981089	+	0.193557i	$0.0620024\pi$
$173$	113.863	+	197.217i	0.658170	+	1.13998i	−0.322919	+	0.946426i	$0.604664\pi$
$174$		−	9.94644i		−	0.0571635i
$175$	−100.806	−	58.2003i	−0.576034	−	0.332573i
$176$			225.269i			1.27994i
$177$	−18.3634	+	31.8063i	−0.103748	+	0.179696i
$178$	−128.499	+	222.567i	−0.721904	+	1.25037i
$179$			262.287i			1.46529i	0.680610	+	0.732646i	$0.261715\pi$
$179$			262.287i			1.46529i	−0.680610	+	0.732646i	$0.738285\pi$
$180$	208.000			1.15556
$181$	−39.9425	+	69.1825i	−0.220677	+	0.382224i	−0.955014	−	0.296562i	$-0.904160\pi$
$181$	−39.9425	+	69.1825i	−0.220677	+	0.382224i	0.734337	+	0.678785i	$0.237493\pi$
$182$	−39.1366	−	22.5956i	−0.215037	−	0.124151i
$183$			39.2987i			0.214747i
$184$	−173.180	−	99.9856i	−0.941196	−	0.543400i
$185$	−12.6594	−	21.9268i	−0.0684293	−	0.118523i
$186$	−56.4317	−	97.7425i	−0.303396	−	0.525497i
$187$	328.657	−	189.750i	1.75753	−	1.01471i
$188$	76.6812	+	44.2719i	0.407879	+	0.235489i
$189$	−85.9327			−0.454670
$190$	−97.5445	−	266.866i	−0.513392	−	1.40456i
$191$		−	233.144i		−	1.22065i	−0.792151	−	0.610325i	$-0.791039\pi$
$191$		−	233.144i		−	1.22065i	0.792151	−	0.610325i	$-0.208961\pi$
$192$	79.2712	−	45.7673i	0.412871	−	0.238371i
$193$	61.4772	+	106.482i	0.318535	+	0.551719i	0.980183	−	0.198096i	$-0.0634759\pi$
$193$	61.4772	+	106.482i	0.318535	+	0.551719i	−0.661648	+	0.749815i	$0.730143\pi$
$194$	−106.046	−	183.676i	−0.546627	−	0.946785i
$195$	55.5683	−	32.0824i	0.284966	−	0.164525i
$196$	139.271			0.710567
$197$	−154.158			−0.782530			−0.391265	−	0.920278i	$-0.627962\pi$
$197$	−154.158			−0.782530			−0.391265	+	0.920278i	$0.627962\pi$
$198$	−169.592	−	97.9141i	−0.856526	−	0.494515i
$199$	−92.9762	−	53.6798i	−0.467217	−	0.269748i	0.247857	−	0.968797i	$-0.420274\pi$
$199$	−92.9762	−	53.6798i	−0.467217	−	0.269748i	−0.715074	+	0.699049i	$0.753607\pi$
$200$	−123.636	+	214.143i	−0.618178	+	1.07072i
$201$	52.8654			0.263012
$202$	133.885	−	231.896i	0.662797	−	1.14800i
$203$	11.3406	+	6.54749i	0.0558649	+	0.0322536i
$204$	−133.545	−	77.1020i	−0.654630	−	0.377951i
$205$	−33.3069	+	57.6893i	−0.162473	+	0.281411i
$206$			206.954i			1.00463i
$207$	150.547	−	86.9181i	0.727278	−	0.419894i
$208$	−48.0000	+	83.1384i	−0.230769	+	0.399704i
$209$	−46.0921	+	263.507i	−0.220537	+	1.26080i
$210$	40.2733	−	69.7554i	0.191778	−	0.332169i
$211$	−117.226	+	67.6803i	−0.555572	+	0.320760i	−0.751366	−	0.659885i	$-0.770605\pi$
$211$	−117.226	+	67.6803i	−0.555572	+	0.320760i	0.195794	+	0.980645i	$0.437271\pi$
$212$	167.818	−	290.669i	0.791593	−	1.37108i
$213$	73.7723	−	127.777i	0.346349	−	0.599893i
$214$			135.573i			0.633520i
$215$	339.362	+	195.931i	1.57843	+	0.911307i
$216$			182.548i			0.845129i
$217$	148.590			0.684747
$218$	49.7267	+	86.1292i	0.228104	+	0.395088i
$219$	11.0347	+	6.37088i	0.0503867	+	0.0290908i
$220$	364.681	−	210.549i	1.65764	−	0.957040i
$221$	161.727			0.731795
$222$	8.38820	−	4.84293i	0.0377847	−	0.0218150i
$223$	−118.943	+	68.6715i	−0.533375	+	0.307944i	−0.742390	−	0.669968i	$-0.766308\pi$
$223$	−118.943	+	68.6715i	−0.533375	+	0.307944i	0.209015	+	0.977912i	$0.432974\pi$
$224$			120.510i			0.537989i
$225$	−107.477	−	186.156i	−0.477677	−	0.827360i
$226$	−141.818			−0.627512
$227$		−	92.9922i		−	0.409657i	−0.978798	−	0.204829i	$-0.934336\pi$
$227$		−	92.9922i		−	0.409657i	0.978798	−	0.204829i	$-0.0656637\pi$
$228$	102.091	−	37.3162i	0.447768	−	0.163667i
$229$	−164.182			−0.716953			−0.358476	−	0.933539i	$-0.616704\pi$
$229$	−164.182			−0.716953			−0.358476	+	0.933539i	$0.616704\pi$
$230$			373.807i			1.62525i
$231$	−65.6734	+	37.9166i	−0.284300	+	0.164141i
$232$	13.9089	−	24.0909i	0.0599522	−	0.103840i
$233$	−27.2723	−	47.2369i	−0.117048	−	0.202734i	0.801548	−	0.597930i	$-0.204010\pi$
$233$	−27.2723	−	47.2369i	−0.117048	−	0.202734i	−0.918597	+	0.395196i	$0.870677\pi$
$234$	−41.7267	−	72.2728i	−0.178319	−	0.308858i
$235$		−	165.515i		−	0.704321i
$236$	−88.9545	+	51.3579i	−0.376926	+	0.217618i
$237$	−92.4079	+	160.055i	−0.389907	+	0.675338i
$238$	175.818	−	101.508i	0.738730	−	0.426506i
$239$			285.524i			1.19466i	0.801995	+	0.597331i	$0.203772\pi$
$239$			285.524i			1.19466i	−0.801995	+	0.597331i	$0.796228\pi$
$240$	−148.182	−	85.5530i	−0.617426	−	0.356471i
$241$	87.8861	−	152.223i	0.364673	−	0.631632i	−0.624051	−	0.781384i	$-0.714514\pi$
$241$	87.8861	−	152.223i	0.364673	−	0.631632i	0.988724	+	0.149752i	$0.0478475\pi$
$242$	−154.455			−0.638246
$243$	−214.954	−	124.104i	−0.884586	−	0.510716i
$244$	−54.9545	+	95.1839i	−0.225223	+	0.390098i
$245$	−130.170	−	225.462i	−0.531307	−	0.920251i
$246$	−22.0694	−	12.7418i	−0.0897128	−	0.0517957i
$247$	−73.1584	+	87.4291i	−0.296188	+	0.353964i
$248$		−	315.652i		−	1.27279i
$249$	19.4327	+	33.6584i	0.0780430	+	0.135174i
$250$	88.3644			0.353458
$251$	140.124	+	80.9005i	0.558262	+	0.322313i	0.752448	−	0.658652i	$-0.228873\pi$
$251$	140.124	+	80.9005i	0.558262	+	0.322313i	−0.194186	+	0.980965i	$0.562206\pi$
$252$	−90.7246	−	52.3799i	−0.360018	−	0.207857i
$253$	175.966	−	304.783i	0.695519	−	1.20467i
$254$	40.4079	+	23.3295i	0.159086	+	0.0918484i
$255$			288.254i			1.13041i
$256$	256.000			1.00000
$257$	154.862	−	268.229i	0.602577	−	1.04369i	−0.389852	−	0.920877i	$-0.627474\pi$
$257$	154.862	−	268.229i	0.602577	−	1.04369i	0.992429	−	0.122817i	$-0.0391927\pi$
$258$	−74.9545	+	129.825i	−0.290521	+	0.503197i
$259$			12.7519i			0.0492352i
$260$	179.453			0.690205
$261$	12.0911	+	20.9424i	0.0463260	+	0.0802391i
$262$	47.8872	−	27.6477i	0.182775	−	0.105525i
$263$	−171.238	+	98.8641i	−0.651093	+	0.375909i	−0.788875	−	0.614554i	$-0.789336\pi$
$263$	−171.238	+	98.8641i	−0.651093	+	0.375909i	0.137782	+	0.990463i	$0.456003\pi$
$264$	80.5466	+	139.511i	0.305101	+	0.528450i
$265$	−627.406			−2.36757
$266$	−24.6573	+	140.965i	−0.0926968	+	0.529943i
$267$			183.783i			0.688325i
$268$	128.043	+	73.9259i	0.477774	+	0.275843i
$269$	77.6356	+	134.469i	0.288608	+	0.499884i	0.973478	−	0.228782i	$-0.0734742\pi$
$269$	77.6356	+	134.469i	0.288608	+	0.499884i	−0.684870	+	0.728666i	$0.740141\pi$
$270$	295.521	−	170.619i	1.09452	−	0.631922i
$271$	52.0098	−	30.0279i	0.191918	−	0.110804i	−0.400962	−	0.916095i	$-0.631324\pi$
$271$	52.0098	−	30.0279i	0.191918	−	0.110804i	0.592880	+	0.805291i	$0.297991\pi$
$272$	−215.636	−	373.492i	−0.792778	−	1.37313i
$273$	−32.3168			−0.118376
$274$	198.818	−	344.363i	0.725612	−	1.25680i
$275$	−376.874	−	217.588i	−1.37045	−	0.791231i
$276$	−143.002			−0.518123
$277$	399.430			1.44198			0.720992	−	0.692943i	$-0.243686\pi$
$277$	399.430			1.44198			0.720992	+	0.692943i	$0.243686\pi$
$278$	465.475	+	268.742i	1.67437	+	0.966699i
$279$	237.636	+	137.199i	0.851741	+	0.491753i
$280$	195.089	−	112.635i	0.696747	−	0.402267i
$281$	−228.999	+	396.638i	−0.814943	+	1.41152i	0.0944260	+	0.995532i	$0.469898\pi$
$281$	−228.999	+	396.638i	−0.814943	+	1.41152i	−0.909369	+	0.415991i	$0.863435\pi$
$282$	63.3188			0.224535
$283$	362.237	−	209.137i	1.27999	−	0.739001i	0.303142	−	0.952945i	$-0.401964\pi$
$283$	362.237	−	209.137i	1.27999	−	0.739001i	0.976846	+	0.213944i	$0.0686311\pi$
$284$	357.362	−	206.323i	1.25832	−	0.726490i
$285$	−155.830	−	130.394i	−0.546771	−	0.457523i
$286$	−146.317	−	84.4760i	−0.511597	−	0.295371i
$287$	29.0554	−	16.7751i	0.101238	−	0.0584499i
$288$	−111.271	+	192.727i	−0.386358	+	0.669192i
$289$	−218.771	+	378.923i	−0.756994	+	1.31115i
$290$	−52.0000			−0.179310
$291$	−131.349	−	75.8346i	−0.451372	−	0.260600i
$292$	17.8178	+	30.8613i	0.0610199	+	0.105690i
$293$	−123.794			−0.422505			−0.211253	−	0.977432i	$-0.567754\pi$
$293$	−123.794			−0.422505			−0.211253	+	0.977432i	$0.567754\pi$
$294$	86.2516	−	49.7974i	0.293373	−	0.169379i
$295$	166.283	+	96.0036i	0.563672	+	0.325436i
$296$	27.0890			0.0915170
$297$	−321.269			−1.08171
$298$	72.4317	+	125.455i	0.243059	+	0.420991i
$299$	129.885	−	74.9892i	0.434398	−	0.250800i
$300$			176.827i			0.589423i
$301$	−98.6812	−	170.921i	−0.327844	−	0.567843i
$302$		−	78.9129i		−	0.261301i
$303$		−	191.486i		−	0.631967i
$304$	299.453	+	52.3799i	0.985044	+	0.172302i
$305$	205.453			0.673618
$306$	374.907			1.22519
$307$	−146.783	+	84.7453i	−0.478121	+	0.276043i	−0.719633	−	0.694355i	$-0.755690\pi$
$307$	−146.783	+	84.7453i	−0.478121	+	0.276043i	0.241512	+	0.970398i	$0.422357\pi$
$308$	−212.087			−0.688594
$309$	73.9979	+	128.168i	0.239475	+	0.414784i
$310$	−510.998	+	295.025i	−1.64838	+	0.951693i
$311$			407.488i			1.31025i	0.755520	+	0.655125i	$0.227384\pi$
$311$			407.488i			1.31025i	−0.755520	+	0.655125i	$0.772616\pi$
$312$			68.6509i			0.220035i
$313$	286.361	−	495.992i	0.914892	−	1.58464i	0.107833	−	0.994169i	$-0.465609\pi$
$313$	286.361	−	495.992i	0.914892	−	1.58464i	0.807059	−	0.590471i	$-0.201058\pi$
$314$	−101.909	−	176.511i	−0.324551	−	0.562138i
$315$			195.828i			0.621677i
$316$	−447.636	+	258.443i	−1.41657	+	0.817856i
$317$	−264.453	+	458.047i	−0.834238	+	1.44494i	0.0604115	+	0.998174i	$0.480759\pi$
$317$	−264.453	+	458.047i	−0.834238	+	1.44494i	−0.894649	+	0.446769i	$0.852575\pi$
$318$		−	240.018i		−	0.754772i
$319$	42.3980	+	24.4785i	0.132909	+	0.0767352i
$320$	−239.271	−	414.430i	−0.747723	−	1.29509i
$321$	48.4752	+	83.9614i	0.151013	+	0.261562i
$322$	94.1346	−	163.046i	0.292343	−	0.506354i
$323$	−175.818	−	481.009i	−0.544328	−	1.48919i
$324$	−59.9089	−	103.765i	−0.184904	−	0.320263i
$325$	−92.7267	−	160.607i	−0.285313	−	0.494177i
$326$		−	381.126i		−	1.16910i
$327$	61.5921	+	35.5602i	0.188355	+	0.108747i
$328$	−35.6356	−	61.7227i	−0.108645	−	0.188179i
$329$	−41.6812	+	72.1939i	−0.126690	+	0.219434i
$330$	150.566	−	260.788i	0.456261	−	0.790268i
$331$			59.2704i			0.179065i	0.995984	+	0.0895324i	$0.0285373\pi$
$331$			59.2704i			0.179065i	−0.995984	+	0.0895324i	$0.971463\pi$
$332$			108.697i			0.327401i
$333$	−11.7743	+	20.3937i	−0.0353583	+	0.0612425i
$334$	−513.362	−	296.390i	−1.53701	−	0.887395i
$335$		−	276.380i		−	0.825016i
$336$	43.0890	+	74.6324i	0.128241	+	0.222120i
$337$	−135.203	−	234.178i	−0.401196	−	0.694891i	0.592675	−	0.805442i	$-0.298072\pi$
$337$	−135.203	−	234.178i	−0.401196	−	0.694891i	−0.993870	+	0.110551i	$0.964739\pi$
$338$	133.000	+	230.363i	0.393491	+	0.681547i
$339$	−87.8287	+	50.7079i	−0.259082	+	0.149581i
$340$	−403.089	+	698.171i	−1.18556	+	2.05344i
$341$	555.521			1.62909
$342$	−169.592	+	202.674i	−0.495883	+	0.592614i
$343$			315.652i			0.920267i
$344$	−363.089	+	209.630i	−1.05549	+	0.609388i
$345$	133.657	+	231.501i	0.387413	+	0.671018i
$346$	227.727	+	394.434i	0.658170	+	1.13998i
$347$	292.649	−	168.961i	0.843368	−	0.486919i	−0.0150399	−	0.999887i	$-0.504788\pi$
$347$	292.649	−	168.961i	0.843368	−	0.486919i	0.858407	+	0.512968i	$0.171454\pi$
$348$		−	19.8929i		−	0.0571635i
$349$	−156.729			−0.449080			−0.224540	−	0.974465i	$-0.572088\pi$
$349$	−156.729			−0.449080			−0.224540	+	0.974465i	$0.572088\pi$
$350$	−201.612	−	116.401i	−0.576034	−	0.332573i
$351$	−118.568	−	68.4555i	−0.337801	−	0.195030i
$352$			450.539i			1.27994i
$353$	13.7723			0.0390149			0.0195074	−	0.999810i	$-0.493790\pi$
$353$	13.7723			0.0390149			0.0195074	+	0.999810i	$0.493790\pi$
$354$	−36.7267	+	63.6125i	−0.103748	+	0.179696i
$355$	−668.020	−	385.681i	−1.88175	−	1.08643i
$356$	−256.998	+	445.133i	−0.721904	+	1.25037i
$357$	72.5901	−	125.730i	0.203334	−	0.352184i
$358$			524.575i			1.46529i
$359$	71.7148	−	41.4046i	0.199763	−	0.115333i	−0.396782	−	0.917913i	$-0.629873\pi$
$359$	71.7148	−	41.4046i	0.199763	−	0.115333i	0.596545	+	0.802580i	$0.296540\pi$
$360$	416.000			1.15556
$361$	339.565	+	122.542i	0.940624	+	0.339451i
$362$	−79.8851	+	138.365i	−0.220677	+	0.382224i
$363$	−95.6553	+	55.2266i	−0.263513	+	0.152139i
$364$	−78.2733	−	45.1911i	−0.215037	−	0.124151i
$365$	33.3069	−	57.6893i	0.0912519	−	0.158053i
$366$			78.5973i			0.214747i
$367$	−261.398	−	150.918i	−0.712256	−	0.411221i	0.0996397	−	0.995024i	$-0.468231\pi$
$367$	−261.398	−	150.918i	−0.712256	−	0.411221i	−0.811896	+	0.583802i	$0.801564\pi$
$368$	−346.360	−	199.971i	−0.941196	−	0.543400i
$369$	61.9565			0.167904
$370$	−25.3188	−	43.8535i	−0.0684293	−	0.118523i
$371$	273.659	+	157.997i	0.737626	+	0.425869i
$372$	−112.863	−	195.485i	−0.303396	−	0.525497i
$373$	301.909			0.809407			0.404704	−	0.914448i	$-0.367375\pi$
$373$	301.909			0.809407			0.404704	+	0.914448i	$0.367375\pi$
$374$	657.315	−	379.501i	1.75753	−	1.01471i
$375$	54.7246	−	31.5953i	0.145932	−	0.0842541i
$376$	153.362	+	88.5438i	0.407879	+	0.235489i
$377$	10.4317	+	18.0682i	0.0276702	+	0.0479262i
$378$	−171.865			−0.454670
$379$		−	498.042i		−	1.31409i	−0.753850	−	0.657047i	$-0.771805\pi$
$379$		−	498.042i		−	1.31409i	0.753850	−	0.657047i	$-0.228195\pi$
$380$	−195.089	−	533.732i	−0.513392	−	1.40456i
$381$	33.3665			0.0875760
$382$		−	466.289i		−	1.22065i
$383$	−30.0771	+	17.3650i	−0.0785303	+	0.0453395i	−0.538751	−	0.842465i	$-0.681104\pi$
$383$	−30.0771	+	17.3650i	−0.0785303	+	0.0453395i	0.460221	+	0.887805i	$0.347770\pi$
$384$	158.542	−	91.5345i	0.412871	−	0.238371i
$385$	198.228	+	343.341i	0.514877	+	0.891794i
$386$	122.954	+	212.963i	0.318535	+	0.551719i
$387$		−	364.465i		−	0.941769i
$388$	−212.091	−	367.353i	−0.546627	−	0.946785i
$389$	−189.046	+	327.436i	−0.485978	+	0.841739i	−0.999870	−	0.0161159i	$-0.994870\pi$
$389$	−189.046	+	327.436i	−0.485978	+	0.841739i	0.513892	+	0.857855i	$0.328203\pi$
$390$	111.137	−	64.1648i	0.284966	−	0.164525i
$391$			673.764i			1.72318i
$392$	278.542			0.710567
$393$	19.7712	−	34.2448i	0.0503084	−	0.0871368i
$394$	−308.317			−0.782530
$395$	836.768	+	483.108i	2.11840	+	1.22306i
$396$	−339.184	−	195.828i	−0.856526	−	0.494515i
$397$	−80.5326	−	139.487i	−0.202853	−	0.351352i	0.746594	−	0.665280i	$-0.231688\pi$
$397$	−80.5326	−	139.487i	−0.202853	−	0.351352i	−0.949447	+	0.313929i	$0.898355\pi$
$398$	−185.952	−	107.360i	−0.467217	−	0.269748i
$399$	35.1325	+	96.1169i	0.0880514	+	0.240894i
$400$	−247.271	+	428.286i	−0.618178	+	1.07072i
$401$	−220.045	−	381.128i	−0.548739	−	0.950445i	−0.998361	−	0.0572256i	$-0.981775\pi$
$401$	−220.045	−	381.128i	−0.548739	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$402$	105.731			0.263012
$403$	205.022	+	118.369i	0.508739	+	0.293720i
$404$	267.770	−	463.792i	0.662797	−	1.14800i
$405$	−111.988	+	193.969i	−0.276514	+	0.478936i
$406$	22.6812	+	13.0950i	0.0558649	+	0.0322536i
$407$			47.6744i			0.117136i
$408$	−267.089	−	154.204i	−0.654630	−	0.377951i
$409$	110.068	−	190.644i	0.269116	−	0.466122i	−0.699518	−	0.714615i	$-0.746602\pi$
$409$	110.068	−	190.644i	0.269116	−	0.466122i	0.968634	+	0.248493i	$0.0799353\pi$
$410$	−66.6139	+	115.379i	−0.162473	+	0.281411i
$411$		−	284.355i		−	0.691860i
$412$			413.909i			1.00463i
$413$	−48.3525	−	83.7490i	−0.117076	−	0.202782i
$414$	301.093	−	173.836i	0.727278	−	0.419894i
$415$	175.966	−	101.594i	0.424015	−	0.244805i
$416$	−96.0000	+	166.277i	−0.230769	+	0.399704i
$417$	384.362			0.921732
$418$	−92.1843	+	527.013i	−0.220537	+	1.26080i
$419$		−	431.538i		−	1.02992i	−0.857213	−	0.514961i	$-0.827806\pi$
$419$		−	431.538i		−	1.02992i	0.857213	−	0.514961i	$-0.172194\pi$
$420$	80.5466	−	139.511i	0.191778	−	0.332169i
$421$	27.0357	+	46.8272i	0.0642179	+	0.111229i	0.896347	−	0.443354i	$-0.146211\pi$
$421$	27.0357	+	46.8272i	0.0642179	+	0.111229i	−0.832129	+	0.554582i	$0.812878\pi$
$422$	−234.451	+	135.361i	−0.555572	+	0.320760i
$423$	−133.319	+	76.9717i	−0.315175	+	0.181966i
$424$	335.636	−	581.338i	0.791593	−	1.37108i
$425$	833.132			1.96031
$426$	147.545	−	255.555i	0.346349	−	0.599893i
$427$	−89.6139	−	51.7386i	−0.209869	−	0.121168i
$428$			271.147i			0.633520i
$429$	−120.820			−0.281631
$430$	678.725	+	391.862i	1.57843	+	0.911307i
$431$	−708.564	−	409.090i	−1.64400	−	0.949164i	−0.979391	−	0.201973i	$-0.935265\pi$
$431$	−708.564	−	409.090i	−1.64400	−	0.949164i	−0.664609	−	0.747191i	$-0.731402\pi$
$432$			365.096i			0.845129i
$433$	186.863	−	323.657i	0.431555	−	0.747475i	−0.565452	−	0.824781i	$-0.691298\pi$
$433$	186.863	−	323.657i	0.431555	−	0.747475i	0.997007	+	0.0773056i	$0.0246317\pi$
$434$	297.180			0.684747
$435$	−32.2039	+	18.5929i	−0.0740320	+	0.0427424i
$436$	99.4534	+	172.258i	0.228104	+	0.395088i
$437$	−364.236	−	304.783i	−0.833491	−	0.697443i
$438$	22.0694	+	12.7418i	0.0503867	+	0.0290908i
$439$	−234.784	+	135.553i	−0.534816	+	0.308776i	−0.742975	−	0.669319i	$-0.766586\pi$
$439$	−234.784	+	135.553i	−0.534816	+	0.308776i	0.208159	+	0.978095i	$0.433253\pi$
$440$	729.362	−	421.098i	1.65764	−	0.957040i
$441$	−121.069	+	209.698i	−0.274534	+	0.475506i
$442$	323.453			0.731795
$443$	379.351	+	219.019i	0.856324	+	0.494399i	0.862780	−	0.505580i	$-0.168722\pi$
$443$	379.351	+	219.019i	0.856324	+	0.494399i	−0.00645570	+	0.999979i	$0.502055\pi$
$444$	16.7764	−	9.68586i	0.0377847	−	0.0218150i
$445$	960.816			2.15914
$446$	−237.885	+	137.343i	−0.533375	+	0.307944i
$447$	89.7148	+	51.7969i	0.200704	+	0.115877i
$448$			241.019i			0.537989i
$449$	−710.180			−1.58169			−0.790846	−	0.612015i	$-0.790359\pi$
$449$	−710.180			−1.58169			−0.790846	+	0.612015i	$0.790359\pi$
$450$	−214.954	−	372.312i	−0.477677	−	0.827360i
$451$	108.627	−	62.7157i	0.240858	−	0.139059i
$452$	−283.636			−0.627512
$453$	−28.2158	−	48.8713i	−0.0622866	−	0.107884i
$454$		−	185.984i		−	0.409657i
$455$			168.952i			0.371323i
$456$	204.182	−	74.6324i	0.447768	−	0.163667i
$457$	320.996			0.702398			0.351199	−	0.936301i	$-0.385774\pi$
$457$	320.996			0.702398			0.351199	+	0.936301i	$0.385774\pi$
$458$	−328.364			−0.716953
$459$	532.657	−	307.530i	1.16047	−	0.670000i
$460$			747.615i			1.62525i
$461$	−415.907	−	720.372i	−0.902184	−	1.56263i	−0.824653	−	0.565639i	$-0.808630\pi$
$461$	−415.907	−	720.372i	−0.902184	−	1.56263i	−0.0775307	−	0.996990i	$-0.524704\pi$
$462$	−131.347	+	75.8331i	−0.284300	+	0.164141i
$463$		−	231.176i		−	0.499299i	−0.968336	−	0.249650i	$-0.919685\pi$
$463$		−	231.176i		−	0.499299i	0.968336	−	0.249650i	$-0.0803155\pi$
$464$	27.8178	−	48.1819i	0.0599522	−	0.103840i
$465$	−210.976	+	365.421i	−0.453712	+	0.785853i
$466$	−54.5445	−	94.4739i	−0.117048	−	0.202734i
$467$			327.762i			0.701846i	0.936404	+	0.350923i	$0.114132\pi$
$467$			327.762i			0.701846i	−0.936404	+	0.350923i	$0.885868\pi$
$468$	−83.4534	−	144.546i	−0.178319	−	0.308858i
$469$	−69.5999	+	120.551i	−0.148401	+	0.257037i
$470$		−	331.031i		−	0.704321i
$471$	−126.226	−	72.8764i	−0.267995	−	0.154727i
$472$	−177.909	+	102.716i	−0.376926	+	0.217618i
$473$	−368.931	−	639.007i	−0.779980	−	1.35097i
$474$	−184.816	+	320.110i	−0.389907	+	0.675338i
$475$	−376.874	+	450.390i	−0.793419	+	0.948189i
$476$	351.636	−	203.017i	0.738730	−	0.426506i
$477$	291.770	+	505.361i	0.611678	+	1.05946i
$478$			571.048i			1.19466i
$479$	67.8178	+	39.1546i	0.141582	+	0.0817424i	0.569118	−	0.822256i	$-0.307285\pi$
$479$	67.8178	+	39.1546i	0.141582	+	0.0817424i	−0.427536	+	0.903998i	$0.640618\pi$
$480$	−296.364	−	171.106i	−0.617426	−	0.356471i
$481$	−10.1584	+	17.5948i	−0.0211193	+	0.0365797i
$482$	175.772	−	304.446i	0.364673	−	0.631632i
$483$		−	134.634i		−	0.278745i
$484$	−308.911			−0.638246
$485$	−396.463	+	686.694i	−0.817450	+	1.41586i
$486$	−429.909	−	248.208i	−0.884586	−	0.510716i
$487$			13.2665i			0.0272413i	0.999907	+	0.0136206i	$0.00433572\pi$
$487$			13.2665i			0.0272413i	−0.999907	+	0.0136206i	$0.995664\pi$
$488$	−109.909	+	190.368i	−0.225223	+	0.390098i
$489$	−136.274	−	236.034i	−0.278680	−	0.482687i
$490$	−260.341	−	450.923i	−0.531307	−	0.920251i
$491$	−139.069	+	80.2917i	−0.283237	+	0.163527i	−0.634888	−	0.772604i	$-0.718954\pi$
$491$	−139.069	+	80.2917i	−0.283237	+	0.163527i	0.351651	+	0.936131i	$0.385620\pi$
$492$	−44.1387	−	25.4835i	−0.0897128	−	0.0517957i
$493$	−93.7267			−0.190115
$494$	−146.317	+	174.858i	−0.296188	+	0.353964i
$495$			732.126i			1.47904i
$496$		−	631.303i		−	1.27279i
$497$	194.249	+	336.450i	0.390844	+	0.676962i
$498$	38.8654	+	67.3169i	0.0780430	+	0.135174i
$499$	−522.621	+	301.735i	−1.04734	+	0.604680i	−0.921902	−	0.387422i	$-0.873366\pi$
$499$	−522.621	+	301.735i	−1.04734	+	0.604680i	−0.125434	+	0.992102i	$0.540032\pi$
$500$	176.729			0.353458
$501$	−423.905			−0.846117
$502$	280.247	+	161.801i	0.558262	+	0.322313i
$503$	−220.170	−	127.115i	−0.437714	−	0.252714i	0.264913	−	0.964272i	$-0.414657\pi$
$503$	−220.170	−	127.115i	−0.437714	−	0.252714i	−0.702628	+	0.711558i	$0.747990\pi$
$504$	−181.449	−	104.760i	−0.360018	−	0.207857i
$505$	−1001.09			−1.98235
$506$	351.933	−	609.565i	0.695519	−	1.20467i
$507$	164.736	+	95.1101i	0.324922	+	0.187594i
$508$	80.8157	+	46.6590i	0.159086	+	0.0918484i
$509$	49.0455	−	84.9494i	0.0963567	−	0.166895i	−0.813817	−	0.581121i	$-0.802614\pi$
$509$	49.0455	−	84.9494i	0.0963567	−	0.166895i	0.910174	+	0.414226i	$0.135948\pi$
$510$			576.509i			1.13041i
$511$	−29.0554	+	16.7751i	−0.0568598	+	0.0328280i
$512$	512.000			1.00000
$513$	−74.7019	+	427.067i	−0.145618	+	0.832489i
$514$	309.725	−	536.459i	0.602577	−	1.04369i
$515$	670.063	−	386.861i	1.30109	−	0.751187i
$516$	−149.909	+	259.650i	−0.290521	+	0.503197i
$517$	−155.830	+	269.905i	−0.301411	+	0.522060i
$518$			25.5038i			0.0492352i
$519$	282.065	+	162.850i	0.543478	+	0.313777i
$520$	358.907			0.690205
$521$	−491.317			−0.943026			−0.471513	−	0.881859i	$-0.656292\pi$
$521$	−491.317			−0.943026			−0.471513	+	0.881859i	$0.656292\pi$
$522$	24.1822	+	41.8848i	0.0463260	+	0.0802391i
$523$	−399.564	−	230.688i	−0.763985	−	0.441087i	0.0667397	−	0.997770i	$-0.478740\pi$
$523$	−399.564	−	230.688i	−0.763985	−	0.441087i	−0.830725	+	0.556683i	$0.812074\pi$
$524$	95.7743	−	55.2953i	0.182775	−	0.105525i
$525$	−166.479			−0.317103
$526$	−342.475	+	197.728i	−0.651093	+	0.375909i
$527$	−921.041	+	531.763i	−1.74771	+	1.00904i
$528$	161.093	+	279.022i	0.305101	+	0.528450i
$529$	47.9099	+	82.9824i	0.0905670	+	0.156867i
$530$	−1254.81			−2.36757
$531$		−	178.583i		−	0.336314i
$532$	−49.3147	+	281.930i	−0.0926968	+	0.529943i
$533$	53.4534			0.100288
$534$			367.565i			0.688325i
$535$	438.950	−	253.428i	0.820468	−	0.473697i
$536$	256.087	+	147.852i	0.477774	+	0.275843i
$537$	187.565	+	324.872i	0.349283	+	0.604977i
$538$	155.271	+	268.938i	0.288608	+	0.499884i
$539$			490.212i			0.909484i
$540$	591.041	−	341.238i	1.09452	−	0.631922i
$541$	−38.1822	+	66.1335i	−0.0705771	+	0.122243i	−0.899154	−	0.437632i	$-0.855817\pi$
$541$	−38.1822	+	66.1335i	−0.0705771	+	0.122243i	0.828577	+	0.559875i	$0.189151\pi$
$542$	104.020	−	60.0558i	0.191918	−	0.110804i
$543$			114.254i			0.210412i
$544$	−431.271	−	746.984i	−0.792778	−	1.37313i
$545$	185.909	−	322.004i	0.341117	−	0.590832i
$546$	−64.6335			−0.118376
$547$	−181.521	−	104.801i	−0.331848	−	0.191592i	0.324813	−	0.945778i	$-0.394698\pi$
$547$	−181.521	−	104.801i	−0.331848	−	0.191592i	−0.656661	+	0.754186i	$0.728032\pi$
$548$	397.636	−	688.725i	0.725612	−	1.25680i
$549$	−95.5445	−	165.488i	−0.174034	−	0.301435i
$550$	−753.748	−	435.177i	−1.37045	−	0.791231i
$551$	42.3980	−	50.6685i	0.0769474	−	0.0919573i
$552$	−286.004			−0.518123
$553$	−243.319	−	421.441i	−0.439998	−	0.762099i
$554$	798.859			1.44198
$555$	−31.3602	−	18.1058i	−0.0565049	−	0.0326231i
$556$	930.950	+	537.484i	1.67437	+	0.966699i
$557$	91.1801	−	157.929i	0.163699	−	0.283534i	−0.772494	−	0.635022i	$-0.780991\pi$
$557$	91.1801	−	157.929i	0.163699	−	0.283534i	0.936192	+	0.351488i	$0.114324\pi$
$558$	475.271	+	274.398i	0.851741	+	0.491753i
$559$		−	314.444i		−	0.562512i
$560$	390.178	−	225.269i	0.696747	−	0.402267i
$561$	271.386	−	470.055i	0.483754	−	0.837887i
$562$	−457.998	+	793.276i	−0.814943	+	1.41152i
$563$		−	483.962i		−	0.859613i	−0.902921	−	0.429807i	$-0.858582\pi$
$563$		−	483.962i		−	0.859613i	0.902921	−	0.429807i	$-0.141418\pi$
$564$	126.638			0.224535
$565$	265.101	+	459.168i	0.469205	+	0.812687i
$566$	724.473	−	418.275i	1.27999	−	0.739001i
$567$	97.6931	−	56.4031i	0.172298	−	0.0994764i
$568$	714.725	−	412.646i	1.25832	−	0.726490i
$569$	64.9586			0.114163			0.0570814	−	0.998370i	$-0.481821\pi$
$569$	64.9586			0.114163			0.0570814	+	0.998370i	$0.481821\pi$
$570$	−311.659	−	260.788i	−0.546771	−	0.457523i
$571$		−	553.718i		−	0.969733i	−0.874588	−	0.484867i	$-0.838868\pi$
$571$		−	553.718i		−	0.969733i	0.874588	−	0.484867i	$-0.161132\pi$
$572$	−292.634	−	168.952i	−0.511597	−	0.295371i
$573$	−166.725	−	288.776i	−0.290968	−	0.503971i
$574$	58.1108	−	33.5503i	0.101238	−	0.0584499i
$575$	669.101	−	386.306i	1.16365	−	0.671836i
$576$	−222.542	+	385.455i	−0.386358	+	0.669192i
$577$	−21.9979			−0.0381247			−0.0190623	−	0.999818i	$-0.506068\pi$
$577$	−21.9979			−0.0381247			−0.0190623	+	0.999818i	$0.506068\pi$
$578$	−437.542	+	757.846i	−0.756994	+	1.31115i
$579$	152.293	+	87.9264i	0.263028	+	0.151859i
$580$	−104.000			−0.179310
$581$	−102.336			−0.176138
$582$	−262.699	−	151.669i	−0.451372	−	0.260600i
$583$	1023.11	+	590.691i	1.75490	+	1.01319i
$584$	35.6356	+	61.7227i	0.0610199	+	0.105690i
$585$	−156.000	+	270.200i	−0.266667	+	0.461880i
$586$	−247.588			−0.422505
$587$	−838.432	+	484.069i	−1.42833	+	0.824649i	−0.996989	−	0.0775389i	$-0.975294\pi$
$587$	−838.432	+	484.069i	−1.42833	+	0.824649i	−0.431344	+	0.902188i	$0.641960\pi$
$588$	172.503	−	99.5947i	0.293373	−	0.169379i
$589$	129.170	−	738.461i	0.219304	−	1.25375i
$590$	332.566	+	192.007i	0.563672	+	0.325436i
$591$	−190.943	+	110.241i	−0.323084	+	0.186533i
$592$	54.1780			0.0915170
$593$	64.8188	−	112.270i	0.109307	−	0.189325i	−0.806183	−	0.591666i	$-0.798470\pi$
$593$	64.8188	−	112.270i	0.109307	−	0.189325i	0.915490	+	0.402342i	$0.131804\pi$
$594$	−642.538			−1.08171
$595$	−657.315	−	379.501i	−1.10473	−	0.637816i
$596$	144.863	+	250.911i	0.243059	+	0.420991i
$597$	−153.549			−0.257200
$598$	259.770	−	149.978i	0.434398	−	0.250800i
$599$	636.142	+	367.277i	1.06201	+	0.613150i	0.925987	−	0.377556i	$-0.123235\pi$
$599$	636.142	+	367.277i	1.06201	+	0.613150i	0.136020	+	0.990706i	$0.456569\pi$
$600$			353.654i			0.589423i
$601$	964.041			1.60406			0.802031	−	0.597282i	$-0.203753\pi$
$601$	964.041			1.60406			0.802031	+	0.597282i	$0.203753\pi$
$602$	−197.362	−	341.842i	−0.327844	−	0.567843i
$603$	−222.618	+	128.529i	−0.369184	+	0.213149i
$604$		−	157.826i		−	0.261301i
$605$	288.725	+	500.086i	0.477231	+	0.826588i
$606$		−	382.972i		−	0.631967i
$607$		−	526.372i		−	0.867170i	−0.901113	−	0.433585i	$-0.857248\pi$
$607$		−	526.372i		−	0.867170i	0.901113	−	0.433585i	$-0.142752\pi$
$608$	598.907	+	104.760i	0.985044	+	0.172302i
$609$	18.7288			0.0307533
$610$	410.907			0.673618
$611$	−115.022	+	66.4078i	−0.188252	+	0.108687i
$612$	749.814			1.22519
$613$	38.9565	+	67.4747i	0.0635506	+	0.110073i	0.896050	−	0.443953i	$-0.146424\pi$
$613$	38.9565	+	67.4747i	0.0635506	+	0.110073i	−0.832500	+	0.554026i	$0.813091\pi$
$614$	−293.566	+	169.491i	−0.478121	+	0.276043i
$615$			95.2729i			0.154915i
$616$	−424.174			−0.688594
$617$	98.9317	−	171.355i	0.160343	−	0.277722i	−0.774649	−	0.632392i	$-0.782073\pi$
$617$	98.9317	−	171.355i	0.160343	−	0.277722i	0.934992	+	0.354669i	$0.115407\pi$
$618$	147.996	+	256.336i	0.239475	+	0.414784i
$619$		−	86.1017i		−	0.139098i	−0.997579	−	0.0695490i	$-0.977844\pi$
$619$		−	86.1017i		−	0.139098i	0.997579	−	0.0695490i	$-0.0221560\pi$
$620$	−1022.00	+	590.050i	−1.64838	+	0.951693i
$621$	285.190	−	493.963i	0.459243	−	0.795432i
$622$			814.976i			1.31025i
$623$	−419.085	−	241.959i	−0.672688	−	0.388377i
$624$			137.302i			0.220035i
$625$	221.181	+	383.097i	0.353890	+	0.612955i
$626$	572.723	−	991.985i	0.914892	−	1.58464i
$627$	131.347	+	359.344i	0.209485	+	0.573116i
$628$	−203.818	−	353.023i	−0.324551	−	0.562138i
$629$	−45.6356	−	79.0432i	−0.0725526	−	0.125665i
$630$			391.656i			0.621677i
$631$	367.717	+	212.301i	0.582753	+	0.336452i	0.762227	−	0.647310i	$-0.224106\pi$
$631$	367.717	+	212.301i	0.582753	+	0.336452i	−0.179474	+	0.983763i	$0.557440\pi$
$632$	−895.271	+	516.885i	−1.41657	+	0.817856i
$633$	−96.7981	+	167.659i	−0.152920	+	0.264865i
$634$	−528.907	+	916.093i	−0.834238	+	1.44494i
$635$		−	174.440i		−	0.274708i
$636$		−	480.035i		−	0.754772i
$637$	−104.453	+	180.919i	−0.163977	+	0.284017i
$638$	84.7961	+	48.9570i	0.132909	+	0.0767352i
$639$			717.432i			1.12274i
$640$	−478.542	−	828.860i	−0.747723	−	1.29509i
$641$	131.637	+	228.001i	0.205361	+	0.355696i	0.950248	−	0.311495i	$-0.100830\pi$
$641$	131.637	+	228.001i	0.205361	+	0.355696i	−0.744886	+	0.667191i	$0.767496\pi$
$642$	96.9503	+	167.923i	0.151013	+	0.261562i
$643$	71.3256	−	41.1798i	0.110926	−	0.0640433i	−0.443510	−	0.896269i	$-0.646267\pi$
$643$	71.3256	−	41.1798i	0.110926	−	0.0640433i	0.554437	+	0.832226i	$0.312934\pi$
$644$	188.269	−	326.092i	0.292343	−	0.506354i
$645$	560.451			0.868917
$646$	−351.636	−	962.019i	−0.544328	−	1.48919i
$647$		−	149.354i		−	0.230841i	−0.993317	−	0.115421i	$-0.963178\pi$
$647$		−	149.354i		−	0.230841i	0.993317	−	0.115421i	$-0.0368216\pi$
$648$	−119.818	−	207.531i	−0.184904	−	0.320263i
$649$	−180.771	−	313.105i	−0.278538	−	0.482442i
$650$	−185.453	−	321.215i	−0.285313	−	0.494177i
$651$	184.046	−	106.259i	0.282712	−	0.163224i
$652$		−	762.253i		−	1.16910i
$653$	335.540			0.513844			0.256922	−	0.966432i	$-0.417292\pi$
$653$	335.540			0.513844			0.256922	+	0.966432i	$0.417292\pi$
$654$	123.184	+	71.1205i	0.188355	+	0.108747i
$655$	−179.032	−	103.364i	−0.273331	−	0.157808i
$656$	−71.2712	−	123.445i	−0.108645	−	0.188179i
$657$	−61.9565			−0.0943022
$658$	−83.3623	+	144.388i	−0.126690	+	0.219434i
$659$	741.636	+	428.184i	1.12540	+	0.649747i	0.942773	−	0.333436i	$-0.108208\pi$
$659$	741.636	+	428.184i	1.12540	+	0.649747i	0.182623	+	0.983183i	$0.441541\pi$
$660$	301.132	−	521.577i	0.456261	−	0.790268i
$661$	115.830	−	200.623i	0.175234	−	0.303514i	−0.765008	−	0.644021i	$-0.777265\pi$
$661$	115.830	−	200.623i	0.175234	−	0.303514i	0.940242	+	0.340506i	$0.110598\pi$
$662$			118.541i			0.179065i
$663$	200.317	−	115.653i	0.302137	−	0.174439i
$664$			217.394i			0.327401i
$665$	502.499	−	183.673i	0.755638	−	0.276200i
$666$	−23.5487	+	40.7875i	−0.0353583	+	0.0612425i
$667$	−75.2733	+	43.4591i	−0.112854	+	0.0651560i
$668$	−1026.72	−	592.780i	−1.53701	−	0.887395i
$669$	−98.2158	+	170.115i	−0.146810	+	0.254282i
$670$		−	552.761i		−	0.825016i
$671$	−335.032	−	193.431i	−0.499302	−	0.288272i
$672$	86.1780	+	149.265i	0.128241	+	0.222120i
$673$	241.727			0.359178			0.179589	−	0.983742i	$-0.442523\pi$
$673$	241.727			0.359178			0.179589	+	0.983742i	$0.442523\pi$
$674$	−270.406	−	468.357i	−0.401196	−	0.694891i
$675$	−610.803	−	352.647i	−0.904893	−	0.522440i
$676$	266.000	+	460.726i	0.393491	+	0.681547i
$677$	842.356			1.24425			0.622124	−	0.782919i	$-0.286270\pi$
$677$	842.356			1.24425			0.622124	+	0.782919i	$0.286270\pi$
$678$	−175.657	+	101.416i	−0.259082	+	0.149581i
$679$	345.856	−	199.680i	0.509360	−	0.294079i
$680$	−806.178	+	1396.34i	−1.18556	+	2.05344i
$681$	−66.5000	−	115.181i	−0.0976505	−	0.169136i
$682$	1111.04			1.62909
$683$			469.540i			0.687467i	0.939067	+	0.343734i	$0.111692\pi$
$683$			469.540i			0.687467i	−0.939067	+	0.343734i	$0.888308\pi$
$684$	−339.184	+	405.348i	−0.495883	+	0.592614i
$685$	−1486.61			−2.17023
$686$			631.303i			0.920267i
$687$	−203.358	+	117.409i	−0.296009	+	0.170901i
$688$	−726.178	+	419.259i	−1.05549	+	0.609388i
$689$	251.727	+	436.003i	0.365351	+	0.632806i
$690$	267.315	+	463.003i	0.387413	+	0.671018i
$691$		−	627.366i		−	0.907910i	−0.891025	−	0.453955i	$-0.850013\pi$
$691$		−	627.366i		−	0.907910i	0.891025	−	0.453955i	$-0.149987\pi$
$692$	455.453	+	788.868i	0.658170	+	1.13998i
$693$	184.369	−	319.336i	0.266044	−	0.460802i
$694$	585.297	−	337.921i	0.843368	−	0.486919i
$695$		−	2009.45i		−	2.89129i
$696$		−	39.7858i		−	0.0571635i
$697$	−120.067	+	207.963i	−0.172263	+	0.298368i
$698$	−313.458			−0.449080
$699$	−67.5595	−	39.0055i	−0.0966517	−	0.0558019i
$700$	−403.224	−	232.801i	−0.576034	−	0.332573i
$701$	440.075	+	762.232i	0.627782	+	1.08735i	0.987996	+	0.154480i	$0.0493703\pi$
$701$	440.075	+	762.232i	0.627782	+	1.08735i	−0.360214	+	0.932870i	$0.617296\pi$
$702$	−237.137	−	136.911i	−0.337801	−	0.195030i
$703$	63.3742	+	11.0853i	0.0901483	+	0.0157686i
$704$			901.078i			1.27994i
$705$	−118.362	−	205.010i	−0.167890	−	0.290794i
$706$	27.5445			0.0390149
$707$	436.651	+	252.101i	0.617611	+	0.356578i
$708$	−73.4534	+	127.225i	−0.103748	+	0.179696i
$709$	533.689	−	924.376i	0.752735	−	1.30377i	−0.193758	−	0.981049i	$-0.562068\pi$
$709$	533.689	−	924.376i	0.752735	−	1.30377i	0.946493	−	0.322725i	$-0.104599\pi$
$710$	−1336.04	−	771.363i	−1.88175	−	1.08643i
$711$		−	898.663i		−	1.26394i
$712$	−513.996	+	890.267i	−0.721904	+	1.25037i
$713$	−493.135	+	854.134i	−0.691633	+	1.19794i
$714$	145.180	−	251.459i	0.203334	−	0.352184i
$715$			631.646i			0.883421i
$716$			1049.15i			1.46529i
$717$	204.182	+	353.654i	0.284773	+	0.493241i
$718$	143.430	−	82.8091i	0.199763	−	0.115333i
$719$	−517.610	+	298.842i	−0.719902	+	0.415636i	−0.814717	−	0.579859i	$-0.803108\pi$
$719$	−517.610	+	298.842i	−0.719902	+	0.415636i	0.0948144	+	0.995495i	$0.469774\pi$
$720$	832.000			1.15556
$721$	−389.687			−0.540482
$722$	679.130	+	245.083i	0.940624	+	0.339451i
$723$		−	251.394i		−	0.347710i
$724$	−159.770	+	276.730i	−0.220677	+	0.382224i
$725$	53.7386	+	93.0780i	0.0741222	+	0.128383i
$726$	−191.311	+	110.453i	−0.263513	+	0.152139i
$727$	−209.050	+	120.695i	−0.287551	+	0.166018i	−0.636837	−	0.770998i	$-0.719758\pi$
$727$	−209.050	+	120.695i	−0.287551	+	0.166018i	0.349286	+	0.937016i	$0.386424\pi$
$728$	−156.547	−	90.3822i	−0.215037	−	0.124151i
$729$	−85.4037			−0.117152
$730$	66.6139	−	115.379i	0.0912519	−	0.158053i
$731$	1223.36	+	706.306i	1.67354	+	0.966219i
$732$			157.195i			0.214747i
$733$	201.525			0.274932			0.137466	−	0.990507i	$-0.456104\pi$
$733$	201.525			0.274932			0.137466	+	0.990507i	$0.456104\pi$
$734$	−522.796	−	301.836i	−0.712256	−	0.411221i
$735$	−322.461	−	186.173i	−0.438723	−	0.253297i
$736$	−692.720	−	399.942i	−0.941196	−	0.543400i
$737$	−260.207	+	450.692i	−0.353062	+	0.611522i
$738$	123.913			0.167904
$739$	−258.757	+	149.394i	−0.350145	+	0.202156i	−0.664749	−	0.747067i	$-0.731462\pi$
$739$	−258.757	+	149.394i	−0.350145	+	0.202156i	0.314604	+	0.949223i	$0.398128\pi$
$740$	−50.6377	−	87.7070i	−0.0684293	−	0.118523i
$741$	−28.0932	+	160.607i	−0.0379125	+	0.216744i
$742$	547.319	+	315.995i	0.737626	+	0.425869i
$743$	−510.962	+	295.004i	−0.687701	+	0.397045i	−0.802750	−	0.596315i	$-0.796631\pi$
$743$	−510.962	+	295.004i	−0.687701	+	0.397045i	0.115049	+	0.993360i	$0.463298\pi$
$744$	−225.727	−	390.970i	−0.303396	−	0.525497i
$745$	270.794	−	469.029i	0.363482	−	0.629569i
$746$	603.818			0.809407
$747$	−163.664	−	94.4912i	−0.219094	−	0.126494i
$748$	1314.63	−	759.002i	1.75753	−	1.01471i
$749$	−255.280			−0.340827
$750$	109.449	−	63.1906i	0.145932	−	0.0842541i
$751$	−360.208	−	207.966i	−0.479638	−	0.276919i	0.240628	−	0.970617i	$-0.422647\pi$
$751$	−360.208	−	207.966i	−0.479638	−	0.276919i	−0.720266	+	0.693698i	$0.755980\pi$
$752$	306.725	+	177.088i	0.407879	+	0.235489i
$753$	231.412			0.307320
$754$	20.8634	+	36.1364i	0.0276702	+	0.0479262i
$755$	−255.499	+	147.512i	−0.338409	+	0.195381i
$756$	−343.731			−0.454670
$757$	−94.9565	−	164.470i	−0.125438	−	0.217265i	0.796466	−	0.604683i	$-0.206700\pi$
$757$	−94.9565	−	164.470i	−0.125438	−	0.217265i	−0.921904	+	0.387418i	$0.873367\pi$
$758$		−	996.083i		−	1.31409i
$759$		−	503.344i		−	0.663167i
$760$	−390.178	−	1067.46i	−0.513392	−	1.40456i
$761$	−418.493			−0.549925			−0.274962	−	0.961455i	$-0.588665\pi$
$761$	−418.493			−0.549925			−0.274962	+	0.961455i	$0.588665\pi$
$762$	66.7329			0.0875760
$763$	−162.178	+	93.6335i	−0.212553	+	0.122718i
$764$		−	932.577i		−	1.22065i
$765$	−700.816	−	1213.85i	−0.916099	−	1.58673i
$766$	−60.1542	+	34.7301i	−0.0785303	+	0.0453395i
$767$		−	154.074i		−	0.200878i
$768$	317.085	−	183.069i	0.412871	−	0.238371i
$769$	−26.8157	+	46.4462i	−0.0348709	+	0.0603982i	−0.882934	−	0.469497i	$-0.844435\pi$
$769$	−26.8157	+	46.4462i	−0.0348709	+	0.0603982i	0.848063	+	0.529895i	$0.177769\pi$
$770$	396.455	+	686.681i	0.514877	+	0.891794i
$771$		−	442.976i		−	0.574548i
$772$	245.909	+	425.927i	0.318535	+	0.551719i
$773$	−271.667	+	470.541i	−0.351445	+	0.608721i	−0.986503	−	0.163744i	$-0.947643\pi$
$773$	−271.667	+	470.541i	−0.351445	+	0.608721i	0.635058	+	0.772465i	$0.280976\pi$
$774$		−	728.929i		−	0.941769i
$775$	1056.17	+	609.778i	1.36280	+	0.786810i
$776$	−424.182	−	734.705i	−0.546627	−	0.946785i
$777$	9.11906	+	15.7947i	0.0117362	+	0.0203278i
$778$	−378.091	+	654.873i	−0.485978	+	0.841739i
$779$	−58.1108	−	158.982i	−0.0745966	−	0.204084i
$780$	222.273	−	128.330i	0.284966	−	0.164525i
$781$	726.224	+	1257.86i	0.929864	+	1.61057i
$782$			1347.53i			1.72318i
$783$	68.7148	+	39.6725i	0.0877584	+	0.0506673i
$784$	557.085			0.710567
$785$	−380.998	+	659.908i	−0.485348	+	0.840647i
$786$	39.5424	−	68.4895i	0.0503084	−	0.0871368i
$787$			976.098i			1.24028i	0.784492	+	0.620138i	$0.212924\pi$
$787$			976.098i			1.24028i	−0.784492	+	0.620138i	$0.787076\pi$
$788$	−616.634			−0.782530
$789$	−141.398	+	244.909i	−0.179212	+	0.310404i
$790$	1673.54	+	966.217i	2.11840	+	1.22306i
$791$		−	267.038i		−	0.337595i
$792$	−678.369	−	391.656i	−0.856526	−	0.494515i
$793$	−82.4317	−	142.776i	−0.103949	−	0.180045i
$794$	−161.065	−	278.973i	−0.202853	−	0.351352i
$795$	−777.113	+	448.666i	−0.977500	+	0.564360i
$796$	−371.905	−	214.719i	−0.467217	−	0.269748i
$797$	−596.606			−0.748564			−0.374282	−	0.927315i	$-0.622111\pi$
$797$	−596.606			−0.748564			−0.374282	+	0.927315i	$0.622111\pi$
$798$	70.2650	+	192.234i	0.0880514	+	0.240894i
$799$		−	596.662i		−	0.746761i
$800$	−494.542	+	856.573i	−0.618178	+	1.07072i
$801$	−446.820	−	773.915i	−0.557828	−	0.966186i
$802$	−440.089	−	762.257i	−0.548739	−	0.950445i
$803$	−108.627	+	62.7157i	−0.135276	+	0.0781018i
$804$	211.462			0.263012
$805$	−703.865			−0.874367
$806$	410.043	+	236.739i	0.508739	+	0.293720i
$807$	192.321	+	111.037i	0.238316	+	0.137592i
$808$	535.540	−	927.583i	0.662797	−	1.14800i
$809$	718.128			0.887674			0.443837	−	0.896108i	$-0.353617\pi$
$809$	718.128			0.887674			0.443837	+	0.896108i	$0.353617\pi$
$810$	−223.976	+	387.938i	−0.276514	+	0.478936i
$811$	548.471	+	316.660i	0.676290	+	0.390456i	0.798456	−	0.602054i	$-0.205651\pi$
$811$	548.471	+	316.660i	0.676290	+	0.390456i	−0.122166	+	0.992510i	$0.538984\pi$
$812$	45.3623	+	26.1899i	0.0558649	+	0.0322536i
$813$	42.9467	−	74.3859i	0.0528250	−	0.0914955i
$814$			95.3489i			0.117136i
$815$	−1233.99	+	712.442i	−1.51409	+	0.874162i
$816$	−534.178	−	308.408i	−0.654630	−	0.377951i
$817$	−935.224	+	341.842i	−1.14470	+	0.418411i
$818$	220.137	−	381.288i	0.269116	−	0.466122i
$819$	136.087	−	78.5698i	0.166162	−	0.0959339i
$820$	−133.228	+	230.757i	−0.162473	+	0.281411i
$821$	390.770	−	676.834i	0.475969	−	0.824402i	−0.523652	−	0.851932i	$-0.675431\pi$
$821$	390.770	−	676.834i	0.475969	−	0.824402i	0.999621	+	0.0275303i	$0.00876427\pi$
$822$		−	568.709i		−	0.691860i
$823$	−117.748	−	67.9821i	−0.143072	−	0.0826028i	0.426755	−	0.904367i	$-0.359657\pi$
$823$	−117.748	−	67.9821i	−0.143072	−	0.0826028i	−0.569827	+	0.821764i	$0.692990\pi$
$824$			827.817i			1.00463i
$825$	−622.402			−0.754426
$826$	−96.7050	−	167.498i	−0.117076	−	0.202782i
$827$	447.466	+	258.345i	0.541072	+	0.312388i	0.745513	−	0.666491i	$-0.232204\pi$
$827$	447.466	+	258.345i	0.541072	+	0.312388i	−0.204441	+	0.978879i	$0.565538\pi$
$828$	602.186	−	347.672i	0.727278	−	0.419894i
$829$	−1147.72			−1.38447			−0.692233	−	0.721674i	$-0.743373\pi$
$829$	−1147.72			−1.38447			−0.692233	+	0.721674i	$0.743373\pi$
$830$	351.933	−	203.188i	0.424015	−	0.244805i
$831$	494.739	−	285.637i	0.595353	−	0.343727i
$832$	−192.000	+	332.554i	−0.230769	+	0.399704i
$833$	−469.247	−	812.760i	−0.563322	−	0.975703i
$834$	768.725			0.921732
$835$			2216.17i			2.65410i
$836$	−184.369	+	1054.03i	−0.220537	+	1.26080i
$837$	900.336			1.07567
$838$		−	863.075i		−	1.02992i
$839$	−166.461	+	96.1064i	−0.198404	+	0.114549i	−0.595911	−	0.803051i	$-0.703209\pi$
$839$	−166.461	+	96.1064i	−0.198404	+	0.114549i	0.397507	+	0.917599i	$0.369876\pi$
$840$	161.093	−	279.022i	0.191778	−	0.332169i
$841$	414.454	+	717.856i	0.492811	+	0.853575i
$842$	54.0714	+	93.6545i	0.0642179	+	0.111229i
$843$			655.041i			0.777036i
$844$	−468.903	+	270.721i	−0.555572	+	0.320760i
$845$	497.236	−	861.237i	0.588444	−	1.01922i
$846$	−266.638	+	153.943i	−0.315175	+	0.181966i
$847$		−	290.834i		−	0.343369i
$848$	671.271	−	1162.68i	0.791593	−	1.37108i
$849$	299.114	−	518.080i	0.352313	−	0.610224i
$850$	1666.26			1.96031
$851$	−73.3013	−	42.3205i	−0.0861354	−	0.0497303i
$852$	295.089	−	511.109i	0.346349	−	0.599893i
$853$	449.317	+	778.239i	0.526749	+	0.912356i	0.999514	+	0.0311674i	$0.00992250\pi$
$853$	449.317	+	778.239i	0.526749	+	0.912356i	−0.472765	+	0.881188i	$0.656744\pi$
$854$	−179.228	−	103.477i	−0.209869	−	0.121168i
$855$	973.224	+	170.235i	1.13827	+	0.199105i
$856$			542.293i			0.633520i
$857$	−62.9555	−	109.042i	−0.0734603	−	0.127237i	0.826955	−	0.562268i	$-0.190071\pi$
$857$	−62.9555	−	109.042i	−0.0734603	−	0.127237i	−0.900416	+	0.435031i	$0.856738\pi$
$858$	−241.640			−0.281631
$859$	−503.551	−	290.725i	−0.586206	−	0.338446i	0.177390	−	0.984141i	$-0.443235\pi$
$859$	−503.551	−	290.725i	−0.586206	−	0.338446i	−0.763596	+	0.645694i	$0.776568\pi$
$860$	1357.45	+	783.724i	1.57843	+	0.911307i
$861$	23.9922	−	41.5558i	0.0278656	−	0.0482646i
$862$	−1417.13	−	818.179i	−1.64400	−	0.949164i
$863$		−	1700.91i		−	1.97092i	−0.169894	−	0.985462i	$-0.554343\pi$
$863$		−	1700.91i		−	1.97092i	0.169894	−	0.985462i	$-0.445657\pi$
$864$			730.192i			0.845129i
$865$	851.382	−	1474.64i	0.984257	−	1.70478i
$866$	373.727	−	647.314i	0.431555	−	0.747475i
$867$			625.785i			0.721782i
$868$	594.360			0.684747
$869$	−909.675	−	1575.60i	−1.04681	−	1.81312i
$870$	−64.4079	+	37.1859i	−0.0740320	+	0.0427424i
$871$	−192.065	+	110.889i	−0.220511	+	0.127312i
$872$	198.907	+	344.517i	0.228104	+	0.395088i
$873$	737.489			0.844775
$874$	−728.471	−	609.565i	−0.833491	−	0.697443i
$875$			166.387i			0.190156i
$876$	44.1387	+	25.4835i	0.0503867	+	0.0290908i
$877$	−36.2417	−	62.7725i	−0.0413247	−	0.0715764i	0.844623	−	0.535361i	$-0.179824\pi$
$877$	−36.2417	−	62.7725i	−0.0413247	−	0.0715764i	−0.885948	+	0.463785i	$0.846491\pi$
$878$	−469.568	+	271.105i	−0.534816	+	0.308776i
$879$	−153.333	+	88.5267i	−0.174440	+	0.100713i
$880$	1458.72	−	842.195i	1.65764	−	0.957040i
$881$	201.998			0.229283			0.114641	−	0.993407i	$-0.463428\pi$
$881$	201.998			0.229283			0.114641	+	0.993407i	$0.463428\pi$
$882$	−242.139	+	419.397i	−0.274534	+	0.475506i
$883$	752.052	+	434.198i	0.851701	+	0.491730i	0.861225	−	0.508225i	$-0.169698\pi$
$883$	752.052	+	434.198i	0.851701	+	0.491730i	−0.00952321	+	0.999955i	$0.503031\pi$
$884$	646.907			0.731795
$885$	274.614			0.310298
$886$	758.703	+	438.037i	0.856324	+	0.494399i
$887$	−511.770	−	295.471i	−0.576968	−	0.333112i	0.182960	−	0.983120i	$-0.441432\pi$
$887$	−511.770	−	295.471i	−0.576968	−	0.333112i	−0.759927	+	0.650008i	$0.774766\pi$
$888$	33.5528	−	19.3717i	0.0377847	−	0.0218150i
$889$	−43.9286	+	76.0865i	−0.0494135	+	0.0855866i
$890$	1921.63			2.15914
$891$	365.237	−	210.869i	0.409918	−	0.236666i
$892$	−475.770	+	274.686i	−0.533375	+	0.307944i
$893$	322.554	+	269.905i	0.361203	+	0.302245i
$894$	179.430	+	103.594i	0.200704	+	0.115877i
$895$	1698.43	−	980.591i	1.89769	−	1.09563i
$896$			482.038i			0.537989i
$897$	107.252	−	185.765i	0.119567	−	0.207096i
$898$	−1420.36			−1.58169
$899$	−118.818	−	68.5995i	−0.132167	−	0.0763064i
$900$	−429.909	−	744.624i	−0.477677	−	0.827360i
$901$	−2261.72			−2.51023
$902$	217.254	−	125.431i	0.240858	−	0.139059i
$903$	−244.455	−	141.136i	−0.270715	−	0.156297i
$904$	−567.271			−0.627512
$905$	597.319			0.660021
$906$	−56.4317	−	97.7425i	−0.0622866	−	0.107884i
$907$	774.413	−	447.107i	0.853818	−	0.492952i	−0.00811954	−	0.999967i	$-0.502585\pi$
$907$	774.413	−	447.107i	0.853818	−	0.492952i	0.861937	+	0.507015i	$0.169251\pi$
$908$		−	371.969i		−	0.409657i
$909$	465.549	+	806.354i	0.512155	+	0.887078i
$910$			337.904i			0.371323i
$911$			1132.77i			1.24343i	0.783242	+	0.621717i	$0.213564\pi$
$911$			1132.77i			1.24343i	−0.783242	+	0.621717i	$0.786436\pi$
$912$	408.364	−	149.265i	0.447768	−	0.163667i
$913$	−382.596			−0.419054
$914$	641.992			0.702398
$915$	254.477	−	146.922i	0.278117	−	0.160571i
$916$	−656.729			−0.716953
$917$	52.0595	+	90.1697i	0.0567716	+	0.0983312i
$918$	1065.31	−	615.060i	1.16047	−	0.670000i
$919$			103.477i			0.112598i	0.998414	+	0.0562988i	$0.0179299\pi$
$919$			103.477i			0.112598i	−0.998414	+	0.0562988i	$0.982070\pi$
$920$			1495.23i			1.62525i
$921$	−121.205	+	209.933i	−0.131601	+	0.227940i
$922$	−831.814	−	1440.74i	−0.902184	−	1.56263i
$923$			618.970i			0.670606i
$924$	−262.694	+	151.666i	−0.284300	+	0.164141i
$925$	−52.3307	+	90.6395i	−0.0565738	+	0.0979887i
$926$		−	462.351i		−	0.499299i
$927$	−623.215	−	359.814i	−0.672293	−	0.388148i
$928$	55.6356	−	96.3637i	0.0599522	−	0.103840i
$929$	622.997	+	1079.06i	0.670610	+	1.16153i	0.977731	+	0.209861i	$0.0673010\pi$
$929$	622.997	+	1079.06i	0.670610	+	1.16153i	−0.307121	+	0.951670i	$0.599366\pi$
$930$	−421.952	+	730.843i	−0.453712	+	0.785853i
$931$	651.644	+	113.985i	0.699940	+	0.122432i
$932$	−109.089	−	188.948i	−0.117048	−	0.202734i
$933$	291.400	+	504.720i	0.312326	+	0.540964i
$934$			655.524i			0.701846i
$935$	−2457.45	−	1418.81i	−2.62828	−	1.51744i
$936$	−166.907	−	289.091i	−0.178319	−	0.308858i
$937$	−831.676	+	1440.51i	−0.887594	+	1.53736i	−0.0448835	+	0.998992i	$0.514292\pi$
$937$	−831.676	+	1440.51i	−0.887594	+	1.53736i	−0.842711	+	0.538366i	$0.819042\pi$
$938$	−139.200	+	241.101i	−0.148401	+	0.257037i
$939$		−	819.123i		−	0.872336i
$940$		−	662.062i		−	0.704321i
$941$	−156.636	+	271.301i	−0.166457	+	0.288311i	−0.937172	−	0.348869i	$-0.886566\pi$
$941$	−156.636	+	271.301i	−0.166457	+	0.288311i	0.770715	+	0.637180i	$0.219899\pi$
$942$	−252.451	−	145.753i	−0.267995	−	0.154727i
$943$			222.690i			0.236151i
$944$	−355.818	+	205.432i	−0.376926	+	0.217618i
$945$	321.269	+	556.454i	0.339967	+	0.588841i
$946$	−737.861	−	1278.01i	−0.779980	−	1.35097i
$947$	918.950	−	530.556i	0.970380	−	0.560249i	0.0710283	−	0.997474i	$-0.477372\pi$
$947$	918.950	−	530.556i	0.970380	−	0.560249i	0.899352	+	0.437225i	$0.144039\pi$
$948$	−369.631	+	640.220i	−0.389907	+	0.675338i
$949$	−53.4534			−0.0563260
$950$	−753.748	+	900.779i	−0.793419	+	0.948189i
$951$			756.457i			0.795433i
$952$	703.271	−	406.034i	0.738730	−	0.426506i
$953$	−649.318	−	1124.65i	−0.681341	−	1.18012i	−0.974572	−	0.224075i	$-0.928064\pi$
$953$	−649.318	−	1124.65i	−0.681341	−	1.18012i	0.293231	−	0.956042i	$-0.405269\pi$
$954$	583.540	+	1010.72i	0.611678	+	1.05946i
$955$	−1509.72	+	871.636i	−1.58086	+	0.912708i
$956$			1142.10i			1.19466i
$957$	70.0197			0.0731658
$958$	135.636	+	78.3093i	0.141582	+	0.0817424i
$959$	648.422	+	374.367i	0.676144	+	0.390372i
$960$	−592.729	−	342.212i	−0.617426	−	0.356471i
$961$	−595.812			−0.619991
$962$	−20.3168	+	35.1897i	−0.0211193	+	0.0365797i
$963$	−408.261	−	235.710i	−0.423947	−	0.244766i
$964$	351.545	−	608.893i	0.364673	−	0.631632i
$965$	459.679	−	796.188i	0.476351	−	0.825065i
$966$		−	269.268i		−	0.278745i
$967$	−312.980	+	180.699i	−0.323661	+	0.186866i	−0.653023	−	0.757338i	$-0.726500\pi$
$967$	−312.980	+	180.699i	−0.323661	+	0.186866i	0.329362	+	0.944204i	$0.393166\pi$
$968$	−617.822			−0.638246
$969$	−561.746	−	470.055i	−0.579718	−	0.485092i
$970$	−792.926	+	1373.39i	−0.817450	+	1.41586i
$971$	−1318.71	+	761.356i	−1.35809	+	0.784095i	−0.989367	−	0.145443i	$-0.953539\pi$
$971$	−1318.71	+	761.356i	−1.35809	+	0.784095i	−0.368726	+	0.929538i	$0.620206\pi$
$972$	−859.818	−	496.416i	−0.884586	−	0.510716i
$973$	−506.032	+	876.472i	−0.520074	+	0.900794i
$974$			26.5330i			0.0272413i
$975$	−229.705	−	132.620i	−0.235595	−	0.136021i
$976$	−219.818	+	380.736i	−0.225223	+	0.390098i
$977$	−12.6874			−0.0129861			−0.00649303	−	0.999979i	$-0.502067\pi$
$977$	−12.6874			−0.0129861			−0.00649303	+	0.999979i	$0.502067\pi$
$978$	−272.549	−	472.068i	−0.278680	−	0.482687i
$979$	−1566.80	−	904.590i	−1.60040	−	0.923994i
$980$	−520.681	−	901.846i	−0.531307	−	0.920251i
$981$	−345.822			−0.352520
$982$	−278.139	+	160.583i	−0.283237	+	0.163527i
$983$	726.273	−	419.314i	0.738833	−	0.426566i	−0.0828116	−	0.996565i	$-0.526390\pi$
$983$	726.273	−	419.314i	0.738833	−	0.426566i	0.821645	+	0.570000i	$0.193057\pi$
$984$	−88.2774	−	50.9670i	−0.0897128	−	0.0517957i
$985$	576.339	+	998.248i	0.585115	+	1.01345i
$986$	−187.453			−0.190115
$987$			119.227i			0.120797i
$988$	−292.634	+	349.716i	−0.296188	+	0.353964i
$989$	1310.00			1.32457
$990$			1464.25i			1.47904i
$991$	1478.90	−	853.842i	1.49233	−	0.861597i	0.492368	−	0.870387i	$-0.336131\pi$
$991$	1478.90	−	853.842i	1.49233	−	0.861597i	0.999961	+	0.00879022i	$0.00279805\pi$
$992$		−	1262.61i		−	1.27279i
$993$	42.3851	+	73.4131i	0.0426839	+	0.0739306i
$994$	388.499	+	672.900i	0.390844	+	0.676962i
$995$			802.752i			0.806786i
$996$	77.7309	+	134.634i	0.0780430	+	0.135174i
$997$	329.734	−	571.117i	0.330727	−	0.572835i	−0.651928	−	0.758281i	$-0.726040\pi$
$997$	329.734	−	571.117i	0.330727	−	0.572835i	0.982655	+	0.185446i	$0.0593729\pi$
$998$	−1045.24	+	603.470i	−1.04734	+	0.604680i
$999$			77.2663i			0.0773436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.g.b.7.2	yes	4
4.3	odd	2		76.3.g.a.7.1	✓	4
19.11	even	3		76.3.g.a.11.1	yes	4
76.11	odd	6	inner	76.3.g.b.11.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.g.a.7.1	✓	4	4.3	odd	2
76.3.g.a.11.1	yes	4	19.11	even	3
76.3.g.b.7.2	yes	4	1.1	even	1	trivial
76.3.g.b.11.2	yes	4	76.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(1.23861 - 0.715113i) q^{3} +4.00000 q^{4} +(-3.73861 - 6.47547i) q^{5} +(2.47723 - 1.43023i) q^{6} +3.76593i q^{7} +8.00000 q^{8} +(-3.47723 + 6.02273i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(1.23861 - 0.715113i) q^{3} +4.00000 q^{4} +(-3.73861 - 6.47547i) q^{5} +(2.47723 - 1.43023i) q^{6} +3.76593i q^{7} +8.00000 q^{8} +(-3.47723 + 6.02273i) q^{9} +(-7.47723 - 12.9509i) q^{10} +14.0793i q^{11} +(4.95445 - 2.86045i) q^{12} +(-3.00000 + 5.19615i) q^{13} +7.53185i q^{14} +(-9.26139 - 5.34706i) q^{15} +16.0000 q^{16} +(-13.4772 - 23.3432i) q^{17} +(-6.95445 + 12.0455i) q^{18} +(18.7158 + 3.27374i) q^{19} +(-14.9545 - 25.9019i) q^{20} +(2.69306 + 4.66452i) q^{21} +28.1587i q^{22} +(-21.6475 - 12.4982i) q^{23} +(9.90890 - 5.72091i) q^{24} +(-15.4545 + 26.7679i) q^{25} +(-6.00000 + 10.3923i) q^{26} +22.8185i q^{27} +15.0637i q^{28} +(1.73861 - 3.01137i) q^{29} +(-18.5228 - 10.6941i) q^{30} -39.4565i q^{31} +32.0000 q^{32} +(10.0683 + 17.4388i) q^{33} +(-26.9545 - 46.6865i) q^{34} +(24.3861 - 14.0793i) q^{35} +(-13.9089 + 24.0909i) q^{36} +3.38613 q^{37} +(37.4317 + 6.54749i) q^{38} +8.58136i q^{39} +(-29.9089 - 51.8037i) q^{40} +(-4.45445 - 7.71534i) q^{41} +(5.38613 + 9.32905i) q^{42} +(-45.3861 + 26.2037i) q^{43} +56.3173i q^{44} +52.0000 q^{45} +(-43.2950 - 24.9964i) q^{46} +(19.1703 + 11.0680i) q^{47} +(19.8178 - 11.4418i) q^{48} +34.8178 q^{49} +(-30.9089 + 53.5358i) q^{50} +(-33.3861 - 19.2755i) q^{51} +(-12.0000 + 20.7846i) q^{52} +(41.9545 - 72.6672i) q^{53} +45.6370i q^{54} +(91.1703 - 52.6372i) q^{55} +30.1274i q^{56} +(25.5228 - 9.32905i) q^{57} +(3.47723 - 6.02273i) q^{58} +(-22.2386 + 12.8395i) q^{59} +(-37.0455 - 21.3883i) q^{60} +(-13.7386 + 23.7960i) q^{61} -78.9129i q^{62} +(-22.6812 - 13.0950i) q^{63} +64.0000 q^{64} +44.8634 q^{65} +(20.1366 + 34.8777i) q^{66} +(32.0109 + 18.4815i) q^{67} +(-53.9089 - 93.3730i) q^{68} -35.7505 q^{69} +(48.7723 - 28.1587i) q^{70} +(89.3406 - 51.5808i) q^{71} +(-27.8178 + 48.1819i) q^{72} +(4.45445 + 7.71534i) q^{73} +6.77226 q^{74} +44.2067i q^{75} +(74.8634 + 13.0950i) q^{76} -53.0217 q^{77} +17.1627i q^{78} +(-111.909 + 64.6106i) q^{79} +(-59.8178 - 103.607i) q^{80} +(-14.9772 - 25.9413i) q^{81} +(-8.90890 - 15.4307i) q^{82} +27.1743i q^{83} +(10.7723 + 18.6581i) q^{84} +(-100.772 + 174.543i) q^{85} +(-90.7723 + 52.4074i) q^{86} -4.97322i q^{87} +112.635i q^{88} +(-64.2495 + 111.283i) q^{89} +104.000 q^{90} +(-19.5683 - 11.2978i) q^{91} +(-86.5901 - 49.9928i) q^{92} +(-28.2158 - 48.8713i) q^{93} +(38.3406 + 22.1359i) q^{94} +(-48.7723 - 133.433i) q^{95} +(39.6356 - 22.8836i) q^{96} +(-53.0228 - 91.8381i) q^{97} +69.6356 q^{98} +(-84.7961 - 48.9570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 - 6 * q^3 + 16 * q^4 - 4 * q^5 - 12 * q^6 + 32 * q^8 + 8 * q^9	\( 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9} - 8 q^{10} - 24 q^{12} - 12 q^{13} - 48 q^{15} + 64 q^{16} - 32 q^{17} + 16 q^{18} + 42 q^{19} - 16 q^{20} - 44 q^{21} + 12 q^{23} - 48 q^{24} - 18 q^{25} - 24 q^{26} - 4 q^{29} - 96 q^{30} + 128 q^{32} + 106 q^{33} - 64 q^{34} - 12 q^{35} + 32 q^{36} - 96 q^{37} + 84 q^{38} - 32 q^{40} + 26 q^{41} - 88 q^{42} - 72 q^{43} + 208 q^{45} + 24 q^{46} - 96 q^{48} - 36 q^{49} - 36 q^{50} - 24 q^{51} - 48 q^{52} + 124 q^{53} + 288 q^{55} + 124 q^{57} - 8 q^{58} - 78 q^{59} - 192 q^{60} - 44 q^{61} + 216 q^{63} + 256 q^{64} + 48 q^{65} + 212 q^{66} - 102 q^{67} - 128 q^{68} - 384 q^{69} - 24 q^{70} + 204 q^{71} + 64 q^{72} - 26 q^{73} - 192 q^{74} + 168 q^{76} + 248 q^{77} - 360 q^{79} - 64 q^{80} - 38 q^{81} + 52 q^{82} - 176 q^{84} - 184 q^{85} - 144 q^{86} - 16 q^{89} + 416 q^{90} - 144 q^{91} + 48 q^{92} - 80 q^{93} + 24 q^{95} - 192 q^{96} - 234 q^{97} - 72 q^{98} - 624 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 6 * q^3 + 16 * q^4 - 4 * q^5 - 12 * q^6 + 32 * q^8 + 8 * q^9 - 8 * q^10 - 24 * q^12 - 12 * q^13 - 48 * q^15 + 64 * q^16 - 32 * q^17 + 16 * q^18 + 42 * q^19 - 16 * q^20 - 44 * q^21 + 12 * q^23 - 48 * q^24 - 18 * q^25 - 24 * q^26 - 4 * q^29 - 96 * q^30 + 128 * q^32 + 106 * q^33 - 64 * q^34 - 12 * q^35 + 32 * q^36 - 96 * q^37 + 84 * q^38 - 32 * q^40 + 26 * q^41 - 88 * q^42 - 72 * q^43 + 208 * q^45 + 24 * q^46 - 96 * q^48 - 36 * q^49 - 36 * q^50 - 24 * q^51 - 48 * q^52 + 124 * q^53 + 288 * q^55 + 124 * q^57 - 8 * q^58 - 78 * q^59 - 192 * q^60 - 44 * q^61 + 216 * q^63 + 256 * q^64 + 48 * q^65 + 212 * q^66 - 102 * q^67 - 128 * q^68 - 384 * q^69 - 24 * q^70 + 204 * q^71 + 64 * q^72 - 26 * q^73 - 192 * q^74 + 168 * q^76 + 248 * q^77 - 360 * q^79 - 64 * q^80 - 38 * q^81 + 52 * q^82 - 176 * q^84 - 184 * q^85 - 144 * q^86 - 16 * q^89 + 416 * q^90 - 144 * q^91 + 48 * q^92 - 80 * q^93 + 24 * q^95 - 192 * q^96 - 234 * q^97 - 72 * q^98 - 624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more